Template-Type: ReDIF-Article 1.0 Author-Name: Kanta Naito Author-X-Name-First: Kanta Author-X-Name-Last: Naito Title: On the asymptotic normality of the L₂-Distance Class of Statistics with Estimated Parameters Abstract: In the problem of testing goodness-of-fit, widely used test statistics form the L ₂-distance. This paper studies the L ₂-distance class of statistics for testing goodness-of-fit. The phrase " L ₂-distance class" means they consistently estimate the L ₂-distance which measures the discrepancy between two probability distributions. Especially the case in which statistics include parameter estimators is investigated. It is shown that the proposed statistic has asymptotic normality under both the null and the alternative distribution. This work is essentially a generalization of the result due to Ahmad (1993) for the particular case of Cramér-von Mises statistic and is closely related to that by de Wet and Randles (1987). Several examples that illustrate the theory are also given. Journal: Journal of Nonparametric Statistics Pages: 199-214 Issue: 3 Volume: 8 Year: 1997 Month: 9 X-DOI: 10.1080/10485259708832720 File-URL: http://hdl.handle.net/10.1080/10485259708832720 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:8:y:1997:i:3:p:199-214 Template-Type: ReDIF-Article 1.0 Author-Name: Ansgar Steland Author-X-Name-First: Ansgar Author-X-Name-Last: Steland Title: On a rank test in a two-factor mixed model with varying dependent repeated measurements Abstract: A rank test for the analysis of a two-factor mixed model with data from n experimental units is studied, where for each factor combination an arbitrary number of repeated dependent measurements is observed, which may grow at a rate of n -super- - ½ - δ,0>δ≤ ½. The proposal covers classical experimental designs, for example the one-way layout and the one factor random block design, and can also be used for meta analyses where data from different designs is combined. Assuming a semiparametric model for the dependent data the asymptotic distribution of the proposed test statistic is derived, and consistent estimators for the asymptotic covariances are proposed. The test statistic is simple to use, automatically adapts to certain commonly used experimental designs, and simplifies in designs with identical replications to simple sums of squares of centered scores. A simulation study suggests that the method can be applied even for moderate sample sizes. Furthermore, the results are applied to a real data set from quality control in clinical chemistry. Journal: Journal of Nonparametric Statistics Pages: 215-235 Issue: 3 Volume: 8 Year: 1997 Month: 9 X-DOI: 10.1080/10485259708832721 File-URL: http://hdl.handle.net/10.1080/10485259708832721 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:8:y:1997:i:3:p:215-235 Template-Type: ReDIF-Article 1.0 Author-Name: Ashis K. Gangopadhyay Author-X-Name-First: Ashis K. Author-X-Name-Last: Gangopadhyay Author-Name: Robert disario Author-X-Name-First: Robert Author-X-Name-Last: disario Author-Name: Dipak K. Dey Author-X-Name-First: Dipak K. Author-X-Name-Last: Dey Title: A nonparametric approach to k-sample inference based on entropy-super-* Abstract: Entropy as a measure of uncertainty is no longer restricted to the domain of communication theory. It is being used in several branches of statistics. In this paper we consider nonparametric methods of estimation of entropy. Using nonparametric methods, we also develop a test of the hypothesis of equality of entropy for multiple groups. A simulation study is performed to compare the power of the proposed test with existing parametric and nonparametric procedures. Finally a bootstrap distribution of the proposed test statistic is considered for two data sets as illustrative examples. Journal: Journal of Nonparametric Statistics Pages: 237-252 Issue: 3 Volume: 8 Year: 1997 Month: 9 X-DOI: 10.1080/10485259708832722 File-URL: http://hdl.handle.net/10.1080/10485259708832722 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:8:y:1997:i:3:p:237-252 Template-Type: ReDIF-Article 1.0 Author-Name: A. Quintela-Del-Río Author-X-Name-First: A. Author-X-Name-Last: Quintela-Del-Río Author-Name: Ph. Vieu Author-X-Name-First: Ph. Author-X-Name-Last: Vieu Title: A nonparametric conditional mode estimate Abstract: This paper proposes a new nonparametric estimate of the conditional mode. This mode estimate is obtained from kernel smoothing of the first derivative of the conditional density function with location adaptive bandwidth. We give the rates of convergence of this estimate under general dependence conditions on the sample that make our results valid for nonparametric prediction of time series. As a by-products, we also get rate of convergence of the usual mode of a density function under dependence, and we give some extensions to local bandwidth of recent results on kernel estimation under mixing conditions. Journal: Journal of Nonparametric Statistics Pages: 253-266 Issue: 3 Volume: 8 Year: 1997 Month: 9 X-DOI: 10.1080/10485259708832723 File-URL: http://hdl.handle.net/10.1080/10485259708832723 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:8:y:1997:i:3:p:253-266 Template-Type: ReDIF-Article 1.0 Author-Name: Mark Finkelstein Author-X-Name-First: Mark Author-X-Name-Last: Finkelstein Author-Name: Howard G. Tucker Author-X-Name-First: Howard G. Author-X-Name-Last: Tucker Title: Unconditional limit theorems from conditional limit theorems Abstract: The method of proof developed here may be used to obtain unconditional limit theorems from conditional limit theorems in a variety of settings. It is known that given two samples with the same arbitrary nondegenerate common distribution function, the conditional distribution of the sum of the tied midranks of one sample within the pooled ordered sample, centered on its conditional expectation, and normed by the square root of its conditional variance, given the values of its numbers of ties, is asymptotically normal as the two sample sizes tend to infinity, provided that the proportions of ties obey a certain constraint. In this note the unconditional distribution of this same statistic is shown to be asymptotically normal also. Journal: Journal of Nonparametric Statistics Pages: 267-274 Issue: 3 Volume: 8 Year: 1997 Month: 9 X-DOI: 10.1080/10485259708832724 File-URL: http://hdl.handle.net/10.1080/10485259708832724 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:8:y:1997:i:3:p:267-274 Template-Type: ReDIF-Article 1.0 Author-Name: B. Boukai Author-X-Name-First: B. Author-X-Name-Last: Boukai Author-Name: H. Zhou Author-X-Name-First: H. Author-X-Name-Last: Zhou Title: Nonparametric estimation in a two change-point model Abstract: In this paper we consider a change-point model which consists of two change points and a transition period in between. A nonparametric estimation procedure for the two unknown change points is proposed, based on the weighted Kolmogorov-Smirnov norm. The strong consistency of the resulting estimates is shown along with rate of convergence. Detailed technical proofs for the main results are given as well as results of a simulation study. The estimation procedure is exemplified on the well-known Coal-Mining data. Journal: Journal of Nonparametric Statistics Pages: 275-292 Issue: 3 Volume: 8 Year: 1997 Month: 9 X-DOI: 10.1080/10485259708832725 File-URL: http://hdl.handle.net/10.1080/10485259708832725 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:8:y:1997:i:3:p:275-292 Template-Type: ReDIF-Article 1.0 Author-Name: Chuan-hua Wei Author-X-Name-First: Chuan-hua Author-X-Name-Last: Wei Author-Name: Chunling Liu Author-X-Name-First: Chunling Author-X-Name-Last: Liu Title: Statistical inference on semi-parametric partial linear additive models Abstract: In the framework of partial linear additive models, we first develop a profile least-squares estimation of the parametric component based on Liang et al.'s [(2008), 'Additive Partial Linear Models with Measurement Errors', Biometrika, 95(3), 667-678] work. This estimator is shown to be asymptotically normal and root-n consistent without requirement of undersmoothing of the nonparametric component. Next, when some additional linear restrictions on the parametric component are available, we postulate a restricted profile least-squares estimator for the parametric component and prove the asymptotic normality of the resulting estimator. To check the validity of the linear constraints on the parametric component, we explore a generalised likelihood ratio test statistic and demonstrate that it follows asymptotically chi-squared distribution under the null hypothesis. Thus, the result unveils a new Wilks type of phenomenon. Simulation studies are conducted to illustrate the proposed methods. An application to the crime rate data in Columbus (Ohio) has been carried out. Journal: Journal of Nonparametric Statistics Pages: 809-823 Issue: 4 Volume: 24 Year: 2012 Month: 12 X-DOI: 10.1080/10485252.2012.716155 File-URL: http://hdl.handle.net/10.1080/10485252.2012.716155 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:809-823 Template-Type: ReDIF-Article 1.0 Author-Name: Heng Lian Author-X-Name-First: Heng Author-X-Name-Last: Lian Title: Variable selection in high-dimensional partly linear additive models Abstract: Semiparametric models are particularly useful for high-dimensional regression problems. In this paper, we focus on partly linear additive models with a large number of predictors (can be larger than the sample size) and consider model estimation and variable selection based on polynomial spline expansion for the nonparametric part with adaptive lasso penalty on the linear part. Convergence rates as well as asymptotic normality of the linear part are shown. We also perform some Monte Carlo studies to demonstrate the performance of the estimator. Journal: Journal of Nonparametric Statistics Pages: 825-839 Issue: 4 Volume: 24 Year: 2012 Month: 12 X-DOI: 10.1080/10485252.2012.701300 File-URL: http://hdl.handle.net/10.1080/10485252.2012.701300 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:825-839 Template-Type: ReDIF-Article 1.0 Author-Name: Tianfa Xie Author-X-Name-First: Tianfa Author-X-Name-Last: Xie Author-Name: Zhihua Sun Author-X-Name-First: Zhihua Author-X-Name-Last: Sun Author-Name: Liuquan Sun Author-X-Name-First: Liuquan Author-X-Name-Last: Sun Title: A consistent model specification test for a partial linear model with covariates missing at random Abstract: In this paper, we discuss the model checking problem for a partial linear model when some covariates are missing at random. A weighted model-adjustment method is applied to estimate the regression coefficients and the nonparametric function for the null hypothetical partial linear model. A testing procedure based on a residual-marked empirical process is developed to check the adequacy of the partial linear model. It is shown that the proposed test is consistent and can detect the local alternatives converging to the null hypothetical model at the rate n -super- - 1/2. Since the asymptotic null distribution of the testing statistics is case-dependent, an adjusted wild bootstrap method is used to decide the critical value, which is proved to be consistent. A simulation study and a real data analysis are conducted to show that the proposed procedure works well. Journal: Journal of Nonparametric Statistics Pages: 841-856 Issue: 4 Volume: 24 Year: 2012 Month: 12 X-DOI: 10.1080/10485252.2012.712692 File-URL: http://hdl.handle.net/10.1080/10485252.2012.712692 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:841-856 Template-Type: ReDIF-Article 1.0 Author-Name: Vincent Guigues Author-X-Name-First: Vincent Author-X-Name-Last: Guigues Title: Nonparametric multivariate breakpoint detection for the means, variances, and covariances of a discrete time stochastic process Abstract: We introduce a nonparametric breakpoint detection method for the means and covariances of a multivariate discrete time stochastic process. Breakpoints are defined as left or right endpoints of maximal intervals of local time homogeneity for the means and covariances. The breakpoint detection method is an adaptive algorithm that estimates the last maximal interval of homogeneity. Applied recursively, it allows us to find an arbitrary number of breakpoints. We then study a second breakpoint detection algorithm that makes use of a sliding window. The quality of both methods is analysed. For the adaptive algorithm, we provide the quality of the estimation of the one-step-ahead means and covariance matrix as well as upper bounds on the type I and type II errors when applying the procedure to a change-point model. Regarding the second method, the probability of correctly detecting the breakpoint of a change-point model is bounded from below. Numerical simulations assess the performance of both methods using simulated data. Journal: Journal of Nonparametric Statistics Pages: 857-882 Issue: 4 Volume: 24 Year: 2012 Month: 12 X-DOI: 10.1080/10485252.2012.709246 File-URL: http://hdl.handle.net/10.1080/10485252.2012.709246 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:857-882 Template-Type: ReDIF-Article 1.0 Author-Name: Isabel Casas Author-X-Name-First: Isabel Author-X-Name-Last: Casas Author-Name: Irene Gijbels Author-X-Name-First: Irene Author-X-Name-Last: Gijbels Title: Unstable volatility: the break-preserving local linear estimator Abstract: The objective of this paper is to introduce the break-preserving local linear (BPLL) estimator for the estimation of unstable volatility functions for independent and asymptotically independent processes. Breaks in the structure of the conditional mean and/or the volatility functions are common in Finance. Nonparametric estimators are well suited for these events due to the flexibility of their functional form and their good asymptotic properties. However, the local polynomial kernel estimators are not consistent at points where the volatility function has a break. The estimator presented in this paper generalises the classical local linear (LL). The BPLL estimator maintains the desirable properties of the LL estimator with regard to the bias and the boundary estimation while it estimates the breaks consistently. An extensive Monte Carlo study is shown as well as detailed proofs of the estimator asymptotic behaviour. Journal: Journal of Nonparametric Statistics Pages: 883-904 Issue: 4 Volume: 24 Year: 2012 Month: 12 X-DOI: 10.1080/10485252.2012.720981 File-URL: http://hdl.handle.net/10.1080/10485252.2012.720981 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:883-904 Template-Type: ReDIF-Article 1.0 Author-Name: F. Autin Author-X-Name-First: F. Author-X-Name-Last: Autin Author-Name: J.-M. Freyermuth Author-X-Name-First: J.-M. Author-X-Name-Last: Freyermuth Author-Name: R. von Sachs Author-X-Name-First: R. Author-X-Name-Last: von Sachs Title: Combining thresholding rules: a new way to improve the performance of wavelet estimators Abstract: In this paper, we address the situation where we cannot differentiate wavelet-based threshold procedures because their sets of well-estimated functions (maxisets) are not nested. As a generic solution, we propose to proceed via a combination of these procedures in order to achieve new procedures which perform better in the sense that the involved maxisets contain the union of the previous ones. Throughout the paper we propose illuminating interpretations of the maxiset results and provide conditions to ensure that this combination generates larger maxisets. As an example, we propose to combine vertical- and horizontal-block thresholding procedures that are already known to perform well. We discuss the limitation of our method, and we check our theoretical results through numerical experiments. Journal: Journal of Nonparametric Statistics Pages: 905-922 Issue: 4 Volume: 24 Year: 2012 Month: 12 X-DOI: 10.1080/10485252.2012.709854 File-URL: http://hdl.handle.net/10.1080/10485252.2012.709854 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:905-922 Template-Type: ReDIF-Article 1.0 Author-Name: Ori Davidov Author-X-Name-First: Ori Author-X-Name-Last: Davidov Author-Name: George Iliopoulos Author-X-Name-First: George Author-X-Name-Last: Iliopoulos Title: Estimating a distribution function subject to a stochastic order restriction: a comparative study Abstract: In this article, we compare four nonparametric estimators of a distribution function (DF), estimated under a stochastic order restriction. The estimators are compared by simulation using four criteria: (1) the estimation of cumulative DFs; (2) the estimation of quantiles; (3) the estimation of moments and other functionals; and (4) as tools for testing for stochastic order. Our simulation study shows that estimators based on the pointwise maximum-likelihood estimator (p-MLE) outperform all other estimators when the underlying distributions are 'close' to each other. The gain in efficiency may be as high as 25%. If the DFs are far apart then the p-MLE may not be the best. However, the efficiency loss using the p-MLE relative to the best estimator in each case is generally low (about 5%). We also find that the test based on the p-MLE is the most powerful in the majority of cases although the gain in power relative to other tests is generally small. Journal: Journal of Nonparametric Statistics Pages: 923-933 Issue: 4 Volume: 24 Year: 2012 Month: 12 X-DOI: 10.1080/10485252.2012.710333 File-URL: http://hdl.handle.net/10.1080/10485252.2012.710333 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:923-933 Template-Type: ReDIF-Article 1.0 Author-Name: Marco Di Marzio Author-X-Name-First: Marco Author-X-Name-Last: Di Marzio Author-Name: Agnese Panzera Author-X-Name-First: Agnese Author-X-Name-Last: Panzera Author-Name: Charles C. Taylor Author-X-Name-First: Charles C. Author-X-Name-Last: Taylor Title: Smooth estimation of circular cumulative distribution functions and quantiles Abstract: Smooth nonparametric estimators based on a kernel method are proposed for cumulative distribution functions (CDFs) and quantiles of circular data. A sound motivation for this is that although for euclidean data similar estimators have been widely studied, for circular data nothing similar seems to exist; albeit, remarkably, in the circular-setting local methods are implemented more easily because of the absence of boundaries on the circle. The only alternative to our method seems to be the empirical CDF, that does not take into account circularity of data when the estimate is near the cut-point, as our local method naturally does. The definition of circular CDF is different from its euclidean counterpart in many respects, and this will give rise to estimators exhibiting some 'unusual' features such as, for example, global efficiency measures containing a location parameter and a covariance term. Simulations along with real data case studies illustrate the findings. Journal: Journal of Nonparametric Statistics Pages: 935-949 Issue: 4 Volume: 24 Year: 2012 Month: 12 X-DOI: 10.1080/10485252.2012.721517 File-URL: http://hdl.handle.net/10.1080/10485252.2012.721517 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:935-949 Template-Type: ReDIF-Article 1.0 Author-Name: Fabienne Comte Author-X-Name-First: Fabienne Author-X-Name-Last: Comte Author-Name: Adeline Samson Author-X-Name-First: Adeline Author-X-Name-Last: Samson Title: Nonparametric estimation of random-effects densities in linear mixed-effects model Abstract: We consider a linear mixed-effects model where Y _{k,
j}=α_k+β_k t _j+ϵ_{k, j} is the observed value for individual k at time t _j, k=1, ..., N, j=0, 1, ..., J. The random effects (α_k, β_k)_k are independent and identically distributed random variables with unknown densities f _α and f _β and are independent of noise. We develop nonparametric estimators of these two densities, which involve a cut-off parameter. We study their mean integrated squared risk and propose cut-off selection strategies, depending on the noise distribution assumptions. Finally, in the particular case of fixed interval between times t _j, we show that a completely data-driven strategy can be implemented without any knowledge on the noise density. Intensive simulation experiments illustrate the method. Journal: Journal of Nonparametric Statistics Pages: 951-975 Issue: 4 Volume: 24 Year: 2012 Month: 12 X-DOI: 10.1080/10485252.2012.731056 File-URL: http://hdl.handle.net/10.1080/10485252.2012.731056 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:951-975 Template-Type: ReDIF-Article 1.0 Author-Name: Riina Lemponen Author-X-Name-First: Riina Author-X-Name-Last: Lemponen Author-Name: Denis Larocque Author-X-Name-First: Denis Author-X-Name-Last: Larocque Author-Name: Jaakko Nevalainen Author-X-Name-First: Jaakko Author-X-Name-Last: Nevalainen Author-Name: Hannu Oja Author-X-Name-First: Hannu Author-X-Name-Last: Oja Title: Weighted rank tests and Hodges-Lehmann estimates for the multivariate two-sample location problem with clustered data Abstract: A family of weighted rank tests and corresponding Hodges-Lehmann estimates are proposed for the analysis of multivariate two-sample clustered data. These procedures are a specific case of the nonparametric multivariate methods for clustered data considered by Nevalainen, Larocque, Oja, and Pörsti [(2010), 'Nonparametric Analysis of Clustered Multivariate Data', Journal of the American Statistical Association, 105, 864-871]. This paper provides detailed proofs of their asymptotic properties that have not been previously published. Optimal weights for the procedures are derived and illustrated. The theoretical results are supplemented with simulation studies. Journal: Journal of Nonparametric Statistics Pages: 977-991 Issue: 4 Volume: 24 Year: 2012 Month: 12 X-DOI: 10.1080/10485252.2012.712693 File-URL: http://hdl.handle.net/10.1080/10485252.2012.712693 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:977-991 Template-Type: ReDIF-Article 1.0 Author-Name: Marie-Hélène Roy Author-X-Name-First: Marie-Hélène Author-X-Name-Last: Roy Author-Name: Denis Larocque Author-X-Name-First: Denis Author-X-Name-Last: Larocque Title: Robustness of random forests for regression Abstract: In this paper, we empirically investigate the robustness of random forests for regression problems. We also investigate the performance of six variations of the original random forest method, all aimed at improving robustness. These variations are based on three main ideas: (1) robustify the aggregation method, (2) robustify the splitting criterion and (3) taking a robust transformation of the response. More precisely, with the first idea, we use the median (or weighted median), instead of the mean, to combine the predictions from the individual trees. With the second idea, we use least-absolute deviations from the median, instead of least-squares, as splitting criterion. With the third idea, we build the trees using the ranks of the response instead of the original values. The competing methods are compared via a simulation study with artificial data using two different types of contaminations and also with 13 real data sets. Our results show that all three ideas improve the robustness of the original random forest algorithm. However, a robust aggregation of the individual trees is generally more profitable than a robust splitting criterion. Journal: Journal of Nonparametric Statistics Pages: 993-1006 Issue: 4 Volume: 24 Year: 2012 Month: 12 X-DOI: 10.1080/10485252.2012.715161 File-URL: http://hdl.handle.net/10.1080/10485252.2012.715161 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:993-1006 Template-Type: ReDIF-Article 1.0 Author-Name: S. Georgiadis Author-X-Name-First: S. Author-X-Name-Last: Georgiadis Author-Name: N. Limnios Author-X-Name-First: N. Author-X-Name-Last: Limnios Title: A multidimensional functional central limit theorem for an empirical estimator of a continuous-time semi-Markov kernel Abstract: In this article, we consider the empirical estimator of the kernel of a semi-Markov process on continuous time with finite state space. We obtain a functional central limit theorem for this estimator in multidimensional form. Next, we present the corresponding theorem for the empirical estimator of the conditional sojourn-time distribution function. The proofs of our results are based on semi-martingales. Journal: Journal of Nonparametric Statistics Pages: 1007-1017 Issue: 4 Volume: 24 Year: 2012 Month: 12 X-DOI: 10.1080/10485252.2012.715162 File-URL: http://hdl.handle.net/10.1080/10485252.2012.715162 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:1007-1017 Template-Type: ReDIF-Article 1.0 Author-Name: P. G. Ferrario Author-X-Name-First: P. G. Author-X-Name-Last: Ferrario Author-Name: H. Walk Author-X-Name-First: H. Author-X-Name-Last: Walk Title: Nonparametric partitioning estimation of residual and local variance based on first and second nearest neighbours Abstract: In this paper, we consider first an estimator of the residual variance treated by Evans [(2005), 'Estimating the Variance of Multiplicative Noise', in 18th International Conference on Noise and Fluctuations, ICNF, in AIP Conference Proceedings, 780, pp. 99-102], Evans and Jones [(2008), 'Non-Parametric Estimation of Residual Moments and Covariance', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 464, 2831-2846] and by Liitiäinen, Corona, and Lendasse [(2008), 'On Nonparametric Residual Variance Estimation', Neural Processing Letters, 28, 155-167; (2010), 'Residual Variance Estimation Using a Nearest Neighbour Statistic', Journal of Multivariate Analysis, 101, 811-823], based on first and second nearest neighbours given an independent and identically distributed sample. Its strong consistency and almost sure convergence of the arithmetic means sequence are shown under mere boundedness and square integrability, respectively, of the response variable Y. Moreover, in view of the local variance, a correspondingly modified estimator of local averaging (partitioning) type is proposed, and strong L ₂-consistency for bounded Y, weak L ₂-consistency and optimal rate of convergence (for bounded X under suitable Hölder continuity conditions on regression and local variance functions) under moment conditions on Y are established. Simulation studies illustrate the behaviour of the local variance estimates. Journal: Journal of Nonparametric Statistics Pages: 1019-1039 Issue: 4 Volume: 24 Year: 2012 Month: 12 X-DOI: 10.1080/10485252.2012.716836 File-URL: http://hdl.handle.net/10.1080/10485252.2012.716836 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:1019-1039 Template-Type: ReDIF-Article 1.0 Author-Name: Junlong Li Author-X-Name-First: Junlong Author-X-Name-Last: Li Author-Name: Chunjie Wang Author-X-Name-First: Chunjie Author-X-Name-Last: Wang Author-Name: Jianguo Sun Author-X-Name-First: Jianguo Author-X-Name-Last: Sun Title: Regression analysis of clustered interval-censored failure time data with the additive hazards model Abstract: This paper discusses regression analysis of clustered failure time data, which means that the failure times of interest are clustered into small groups instead of being independent. Clustering occurs in many fields such as medical studies. For the problem, a number of methods have been proposed, but most of them apply only to clustered right-censored data. In reality, the failure time data is often interval-censored. That is, the failure times of interest are known only to lie in certain intervals. We propose an estimating equation-based approach for regression analysis of clustered interval-censored failure time data generated from the additive hazards model. A major advantage of the proposed method is that it does not involve the estimation of any baseline hazard function. Both asymptotic and finite sample properties of the proposed estimates of regression parameters are established and the method is illustrated by the data arising from a lymphatic filariasis study. Journal: Journal of Nonparametric Statistics Pages: 1041-1050 Issue: 4 Volume: 24 Year: 2012 Month: 12 X-DOI: 10.1080/10485252.2012.720256 File-URL: http://hdl.handle.net/10.1080/10485252.2012.720256 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:1041-1050 Template-Type: ReDIF-Article 1.0 Author-Name: Han-Ying Liang Author-X-Name-First: Han-Ying Author-X-Name-Last: Liang Title: Weighted nonparametric regression estimation with truncated and dependent data Abstract: By applying the empirical likelihood method, we construct a new weighted Nadaraya-Watson type estimator of the conditional mean function for a left truncation model. The function includes the regression function, conditional moment as well as conditional distribution function. Under strong mixing assumptions, we obtain the asymptotic normality and weak consistency of the estimator. Finite sample behaviour of the estimator is investigated via simulations too. Journal: Journal of Nonparametric Statistics Pages: 1051-1073 Issue: 4 Volume: 24 Year: 2012 Month: 12 X-DOI: 10.1080/10485252.2012.721516 File-URL: http://hdl.handle.net/10.1080/10485252.2012.721516 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:1051-1073 Template-Type: ReDIF-Article 1.0 Author-Name: Jun Li Author-X-Name-First: Jun Author-X-Name-Last: Li Author-Name: Xin Zhang Author-X-Name-First: Xin Author-X-Name-Last: Zhang Author-Name: Daniel R. Jeske Author-X-Name-First: Daniel R. Author-X-Name-Last: Jeske Title: Nonparametric multivariate CUSUM control charts for location and scale changes Abstract: Among different multivariate control charts, multivariate cumulative sum (CUSUM) control charts are the popular choice for detecting small and moderate changes in the manufacturing process. However, most of CUSUM procedures in the literature were developed under the multivariate normality assumption. This assumption is usually difficult to justify in practice. In this paper, we propose two new nonparametric multivariate CUSUM procedures based on the spatial sign and data depth for detecting location and scale changes. These two procedures can be considered as the nonparametric counterparts of the two parametric multivariate CUSUM procedures developed in Crosier [(1988), 'Multivariate Generalizations for Cumulative Sum Quality-Control Schemes', Technometrics, 30, 291-303]. We show that the two proposed CUSUM procedures are affine invariant and asymptotically distribution-free over a broad family of distributions. In our simulation studies, the proposed CUSUM procedures perform well across a broad range of settings and compare favourably with existing CUSUM procedures for detecting location and scale changes. Journal: Journal of Nonparametric Statistics Pages: 1-20 Issue: 1 Volume: 25 Year: 2013 Month: 3 X-DOI: 10.1080/10485252.2012.726992 File-URL: http://hdl.handle.net/10.1080/10485252.2012.726992 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:1-20 Template-Type: ReDIF-Article 1.0 Author-Name: Jun Mao Author-X-Name-First: Jun Author-X-Name-Last: Mao Author-Name: David R. McDonald Author-X-Name-First: David R. Author-X-Name-Last: McDonald Author-Name: Mahmoud Zarepour Author-X-Name-First: Mahmoud Author-X-Name-Last: Zarepour Title: A nonparametric on-line quality control procedure for vectorial observations Abstract: We consider an on-line nonparametric quality control procedure for multivariate observations. The goal of the procedure is to rapidly detect an out-of-control situation, that is, to detect a change in sampling distribution after a change point. Each successive observation creates a Voronoi cell indexed by the observation number. Suppose observation n+1 falls into the Voronoi cell with index i, where i is from 1 to n. Then observation n+1 has associated rank i. In the on-target situation these ranks are uniformly distributed but in the off-target situation these ranks tend to be large corresponding to the fact that the later off-target observations tend to clump together because later observations fall according to the off-target distribution. We use these ranks in a Cusum procedure. We found that we can approximately predict the on-target average run length (ARL) of our procedure and get reasonable off-target run lengths for any kind of structural break like a change of mean or a change of dispersion. Journal: Journal of Nonparametric Statistics Pages: 21-32 Issue: 1 Volume: 25 Year: 2013 Month: 3 X-DOI: 10.1080/10485252.2012.740039 File-URL: http://hdl.handle.net/10.1080/10485252.2012.740039 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:21-32 Template-Type: ReDIF-Article 1.0 Author-Name: Neelabh Rohan Author-X-Name-First: Neelabh Author-X-Name-Last: Rohan Author-Name: T. V. Ramanathan Author-X-Name-First: T. V. Author-X-Name-Last: Ramanathan Title: Nonparametric estimation of a time-varying GARCH model Abstract: In this paper, a non-stationary time-varying GARCH (tvGARCH) model has been introduced by allowing the parameters of a stationary GARCH model to vary as functions of time. It is shown that the tvGARCH process is locally stationary in the sense that it can be locally approximated by stationary GARCH processes at fixed time points. We develop a two-step local polynomial procedure for the estimation of the parameter functions of the proposed model. Several asymptotic properties of the estimators have been established, including the asymptotic optimality. It is found that the tvGARCH model performs better than many of the standard GARCH models for various real data sets. Journal: Journal of Nonparametric Statistics Pages: 33-52 Issue: 1 Volume: 25 Year: 2013 Month: 3 X-DOI: 10.1080/10485252.2012.728600 File-URL: http://hdl.handle.net/10.1080/10485252.2012.728600 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:33-52 Template-Type: ReDIF-Article 1.0 Author-Name: Yogendra P. Chaubey Author-X-Name-First: Yogendra P. Author-X-Name-Last: Chaubey Author-Name: Christophe Chesneau Author-X-Name-First: Christophe Author-X-Name-Last: Chesneau Author-Name: Esmaeil Shirazi Author-X-Name-First: Esmaeil Author-X-Name-Last: Shirazi Title: Wavelet-based estimation of regression function for dependent biased data under a given random design Abstract: In this article, we consider the estimation of the regression function in a dependent biased model. It is assumed that the observations form a stationary α-mixing sequence. We introduce a new estimator based on a wavelet basis. We explore its asymptotic performances via the supremum norm error and the mean integrated squared error. Fast rates of convergence are established. Journal: Journal of Nonparametric Statistics Pages: 53-71 Issue: 1 Volume: 25 Year: 2013 Month: 3 X-DOI: 10.1080/10485252.2012.734619 File-URL: http://hdl.handle.net/10.1080/10485252.2012.734619 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:53-71 Template-Type: ReDIF-Article 1.0 Author-Name: Hon Keung Tony Ng Author-X-Name-First: Hon Keung Author-X-Name-Last: Tony Ng Author-Name: Ram C. Tripathi Author-X-Name-First: Ram C. Author-X-Name-Last: Tripathi Author-Name: Narayanaswamy Balakrishnan Author-X-Name-First: Narayanaswamy Author-X-Name-Last: Balakrishnan Title: A two-stage Wilcoxon-type nonparametric test for stochastic ordering in two samples Abstract: The Wilcoxon rank-sum test is a well-known nonparametric test for the equality of two distributions. In this article, we study a two-stage nonparametric procedure by first testing symmetry for the two underlying distributions and then using the Wilcoxon-type precedence test based on right-censored samples. Specifically, in the first stage, we use a test of symmetry for the two underlying distributions. Then, in the second stage, the minimal Wilcoxon rank-sum precedence test based on a partial sample is used for testing the equality of the two distributions against the stochastically ordered alternative, in which the size of the partial sample is determined by the outcome in the first stage. A simulation study reveals that the proposed two-stage procedure maintains the nominal level of significance and performs better than the classical Wilcoxon rank-sum test in terms of power in many situations. Finally, a numerical example is presented to illustrate the nonparametric procedures developed here. Journal: Journal of Nonparametric Statistics Pages: 73-89 Issue: 1 Volume: 25 Year: 2013 Month: 3 X-DOI: 10.1080/10485252.2012.735232 File-URL: http://hdl.handle.net/10.1080/10485252.2012.735232 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:73-89 Template-Type: ReDIF-Article 1.0 Author-Name: Mustafa Nadar Author-X-Name-First: Mustafa Author-X-Name-Last: Nadar Title: Multivariate generalisations of k-sample rank tests for umbrella alternatives Abstract: We consider the problem of multivariate generalisation of k-sample rank tests for umbrella alternatives. That is, testing the null hypothesis of equality of medians against the alternatives of interest of the form

for all x and g=1, ..., p; with at least one strict inequality for at least one g when ℓ is known. This is known as umbrella alternatives and from now on ℓ will be referred to as the peak of the umbrella. Sometimes when comparing populations, we are interested in whether the medians of the groups are increasing up to some point then decreasing as the treatment levels are increasing. We propose a multivariate generalisation of umbrella alternatives based on coordinate-wise approach when the peak of the umbrella ℓ is known. Approximate critical values for the small sample null distributions are also discussed. Furthermore, we study the power of the test under location-family alternatives using small sample simulations. Journal: Journal of Nonparametric Statistics Pages: 91-107 Issue: 1 Volume: 25 Year: 2013 Month: 3 X-DOI: 10.1080/10485252.2012.735669 File-URL: http://hdl.handle.net/10.1080/10485252.2012.735669 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:91-107 Template-Type: ReDIF-Article 1.0 Author-Name: Jianqing Fan Author-X-Name-First: Jianqing Author-X-Name-Last: Fan Author-Name: Arnab Maity Author-X-Name-First: Arnab Author-X-Name-Last: Maity Author-Name: Yihui Wang Author-X-Name-First: Yihui Author-X-Name-Last: Wang Author-Name: Yichao Wu Author-X-Name-First: Yichao Author-X-Name-Last: Wu Title: Parametrically guided generalised additive models with application to mergers and acquisitions data Abstract: Generalised nonparametric additive models present a flexible way to evaluate the effects of several covariates on a general outcome of interest via a link function. In this modelling framework, one assumes that the effect of each of the covariates is nonparametric and additive. However, in practice, often there is prior information available about the shape of the regression functions, possibly from pilot studies or exploratory analysis. In this paper, we consider such situations and propose an estimation procedure where the prior information is used as a parametric guide to fit the additive model. Specifically, we first posit a parametric family for each of the regression functions using the prior information (parametric guides). After removing these parametric trends, we then estimate the remainder of the nonparametric functions using a nonparametric generalised additive model and form the final estimates by adding back the parametric trend. We investigate the asymptotic properties of the estimates and show that when a good guide is chosen, the asymptotic variance of the estimates can be reduced significantly while keeping the asymptotic variance same as the unguided estimator. We observe the performance of our method via a simulation study and demonstrate our method by applying to a real data set on mergers and acquisitions. Journal: Journal of Nonparametric Statistics Pages: 109-128 Issue: 1 Volume: 25 Year: 2013 Month: 3 X-DOI: 10.1080/10485252.2012.735233 File-URL: http://hdl.handle.net/10.1080/10485252.2012.735233 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:109-128 Template-Type: ReDIF-Article 1.0 Author-Name: Shuping Jiang Author-X-Name-First: Shuping Author-X-Name-Last: Jiang Author-Name: Lan Xue Author-X-Name-First: Lan Author-X-Name-Last: Xue Title: Lag selection in stochastic additive models Abstract: We studied stochastic additive models (SAM) for nonlinear time series data. We proposed a penalised polynomial spline (PPS) method for estimation and lag selection in SAM. This method approximated the nonparametric functions by polynomial splines and performed variable/lag selection by imposing a penalty on the empirical L ₂ norm of the spline functions. Under geometrically α-mixing condition, we established that the resulting estimator converges at the same rate as in univariate smoothing. Our method also selected the correct model with probability approaching to one as the sample size increased. A coordinate-wise algorithm was developed for finding the solution of the PPS problem. Extensive Monte Carlo studies had been conducted and showed that the proposed procedure worked effectively even with moderate sample size. We also illustrated the proposed method by analysing the US employment time series. Journal: Journal of Nonparametric Statistics Pages: 129-146 Issue: 1 Volume: 25 Year: 2013 Month: 3 X-DOI: 10.1080/10485252.2012.754440 File-URL: http://hdl.handle.net/10.1080/10485252.2012.754440 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:129-146 Template-Type: ReDIF-Article 1.0 Author-Name: Jiahua Chen Author-X-Name-First: Jiahua Author-X-Name-Last: Chen Author-Name: Yi Huang Author-X-Name-First: Yi Author-X-Name-Last: Huang Title: Finite-sample properties of the adjusted empirical likelihood Abstract: Empirical likelihood-based confidence intervals for the population mean have many interesting properties [Owen, A.B. (1988), 'Empirical Likelihood Ratio Confidence Intervals for a Single Functional', Biometrika, 75, 237-249]. Calibrated by χ-super-2 limiting distribution, however, their coverage probabilities are often lower than the nominal when the sample size is small and/or the dimension of the data is high. The application of adjusted empirical likelihood (AEL) is one of the many ways to achieve a more accurate coverage probability. In this paper, we study the finite-sample properties of the AEL. We find that the AEL ratio function decreases when the level of adjustment increases. Thus, the AEL confidence region has higher coverage probabilities when the level of adjustment increases. We also prove that the AEL ratio function increases when the putative population mean moves away from the sample mean. In addition, we show that the AEL confidence region for the population mean is convex. Finally, computer simulations are conducted to further investigate the precision of the coverage probabilities and the sizes of the confidence regions. An application example is also included. Journal: Journal of Nonparametric Statistics Pages: 147-159 Issue: 1 Volume: 25 Year: 2013 Month: 3 X-DOI: 10.1080/10485252.2012.738906 File-URL: http://hdl.handle.net/10.1080/10485252.2012.738906 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:147-159 Template-Type: ReDIF-Article 1.0 Author-Name: Xuemei Hu Author-X-Name-First: Xuemei Author-X-Name-Last: Hu Author-Name: Xiaohui Liu Author-X-Name-First: Xiaohui Author-X-Name-Last: Liu Title: Empirical likelihood confidence regions for semi-varying coefficient models with linear process errors Abstract: In this paper, we apply the empirical likelihood method to semi-varying coefficient models with linear process errors, propose two empirical log-likelihood ratio statistics and show that their limiting distributions are two weighted sums of independent chi-square distributions with 1 degree of freedom. By estimating the unknown weights consistently, we not only construct the empirical likelihood confidence regions for the parametric component, but also construct the point-wise empirical likelihood confidence regions and the simultaneous empirical likelihood confidence bands for the varying-coefficient functions. Monte Carlo simulation results show that the proposed empirical likelihood confidence regions have better coverage probabilities and shorter median lengths than the normal approximation confidence regions ignoring the correlation information. Journal: Journal of Nonparametric Statistics Pages: 161-180 Issue: 1 Volume: 25 Year: 2013 Month: 3 X-DOI: 10.1080/10485252.2012.751385 File-URL: http://hdl.handle.net/10.1080/10485252.2012.751385 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:161-180 Template-Type: ReDIF-Article 1.0 Author-Name: Pierre Vandekerkhove Author-X-Name-First: Pierre Author-X-Name-Last: Vandekerkhove Title: Estimation of a semiparametric mixture of regressions model Abstract: We introduce in this paper a new mixture of regressions model which is a generalisation of the semiparametric two-component mixture model studied in Bordes, Delmas, and Vandekerkhove [(2006b), 'Semiparametric Estimation of a Two-component Mixture Model When a Component is Known', Scandinavian Journal of Statistics, 33, 733-752]. Namely, we consider a two-component mixture of regressions model in which one component is entirely known while the proportion, the slope, the intercept, and the error distribution of the other component are unknown. Our model is said to be semiparametric in the sense that the probability density function (pdf) of the error involved in the unknown regression model cannot be modelled adequately by using a parametric density family. When the pdfs of the errors involved in each regression model are supposed to be zero-symmetric, we propose an estimator of the various (Euclidean and functional) parameters of the model, and establish under mild conditions their almost sure rates of convergence. Finally, the implementation and numerical performances of our method are discussed using several simulated data sets and one real high-density array data set (ChIP-mix model). Journal: Journal of Nonparametric Statistics Pages: 181-208 Issue: 1 Volume: 25 Year: 2013 Month: 3 X-DOI: 10.1080/10485252.2012.741236 File-URL: http://hdl.handle.net/10.1080/10485252.2012.741236 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:181-208 Template-Type: ReDIF-Article 1.0 Author-Name: Dewei Wang Author-X-Name-First: Dewei Author-X-Name-Last: Wang Author-Name: Haiming Zhou Author-X-Name-First: Haiming Author-X-Name-Last: Zhou Author-Name: K. B. Kulasekera Author-X-Name-First: K. B. Author-X-Name-Last: Kulasekera Title: A semi-local likelihood regression estimator of the proportion based on group testing data Abstract: In this paper, we are concerned with the estimation of a proportion based on group testing data where the prevalence of a disease is observed for groups of individuals. Based on the covariates measured on all individuals in every group, we propose a local likelihood estimator of the prevalence probability as a function of the covariate. We show that the proposed estimator has an asymptotic normal distribution. Finite sample performance of the method is exhibited via some simulated examples and a real data analysis. Journal: Journal of Nonparametric Statistics Pages: 209-221 Issue: 1 Volume: 25 Year: 2013 Month: 3 X-DOI: 10.1080/10485252.2012.750726 File-URL: http://hdl.handle.net/10.1080/10485252.2012.750726 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:209-221 Template-Type: ReDIF-Article 1.0 Author-Name: Dmytro Furer Author-X-Name-First: Dmytro Author-X-Name-Last: Furer Author-Name: Michael Kohler Author-X-Name-First: Michael Author-X-Name-Last: Kohler Author-Name: Adam Krzyżak Author-X-Name-First: Adam Author-X-Name-Last: Krzyżak Title: Fixed-design regression estimation based on real and artificial data Abstract: In this article, we study the fixed-design regression estimation based on real and artificial data, where the artificial data comes from previously undertaken similar experiments. A least-squares estimate that gives different weights to the real and artificial data is introduced. It is investigated under which condition the rate of convergence of this estimate is better than the rate of convergence of an ordinary least-squares estimate applied to the real data only. The results are illustrated using simulated and real data. Journal: Journal of Nonparametric Statistics Pages: 223-241 Issue: 1 Volume: 25 Year: 2013 Month: 3 X-DOI: 10.1080/10485252.2012.749257 File-URL: http://hdl.handle.net/10.1080/10485252.2012.749257 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:223-241 Template-Type: ReDIF-Article 1.0 Author-Name: Holger Dette Author-X-Name-First: Holger Author-X-Name-Last: Dette Author-Name: Jens Wagener Author-X-Name-First: Jens Author-X-Name-Last: Wagener Author-Name: Stanislav Volgushev Author-X-Name-First: Stanislav Author-X-Name-Last: Volgushev Title: Nonparametric comparison of quantile curves: a stochastic process approach Abstract: A new test for comparing conditional quantile curves is proposed which is able to detect Pitman alternatives converging to the null hypothesis at the optimal rate. The basic idea of the test is to measure differences between the curves by a process of integrated nonparametric estimates of the quantile curve. We prove weak convergence of this process to a Gaussian process and study the finite sample properties of a Kolmogorov-Smirnov test by means of a simulation study. Journal: Journal of Nonparametric Statistics Pages: 243-260 Issue: 1 Volume: 25 Year: 2013 Month: 3 X-DOI: 10.1080/10485252.2012.732223 File-URL: http://hdl.handle.net/10.1080/10485252.2012.732223 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:243-260 Template-Type: ReDIF-Article 1.0 Author-Name: Benoît Cadre Author-X-Name-First: Benoît Author-X-Name-Last: Cadre Author-Name: Bruno Pelletier Author-X-Name-First: Bruno Author-X-Name-Last: Pelletier Author-Name: Pierre Pudlo Author-X-Name-First: Pierre Author-X-Name-Last: Pudlo Title: Estimation of density level sets with a given probability content Abstract: Given a random vector X valued in ℝ-super- d with density f and an arbitrary probability number p∈(0; 1), we consider the estimation of the upper level set>texlscub>f≥t -super-(p)>/texlscub>of f corresponding to probability content p, that is, such that the probability that X belongs to>texlscub>f≥t -super-(p)>/texlscub>is equal to p. Based on an i.i.d. random sample X ₁, ..., X _n drawn from f, we define the plug-in level set estimate

, where

is a random threshold depending on the sample and [fcirc] _n is a nonparametric kernel density estimate based on the same sample. We establish the exact convergence rate of the Lebesgue measure of the symmetric difference between the estimated and actual level sets. Journal: Journal of Nonparametric Statistics Pages: 261-272 Issue: 1 Volume: 25 Year: 2013 Month: 3 X-DOI: 10.1080/10485252.2012.750319 File-URL: http://hdl.handle.net/10.1080/10485252.2012.750319 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:261-272 Template-Type: ReDIF-Article 1.0 Author-Name: Tao Chen Author-X-Name-First: Tao Author-X-Name-Last: Chen Author-Name: Gautam Tripathi Author-X-Name-First: Gautam Author-X-Name-Last: Tripathi Title: Testing conditional symmetry without smoothing Abstract: We test the assumption of conditional symmetry used to identify and estimate parameters in regression models with endogenous regressors, without making any distributional assumptions. The Kolmogorov-Smirnov-type statistic we propose is consistent, computationally tractable because it does not require optimisation over an uncountable set, free of any kind of nonparametric smoothing, and can detect n -super-1/2-deviations from the null. Results from a simulation experiment suggest that our test can work very well in moderately sized samples. Journal: Journal of Nonparametric Statistics Pages: 273-313 Issue: 2 Volume: 25 Year: 2013 Month: 6 X-DOI: 10.1080/10485252.2012.752083 File-URL: http://hdl.handle.net/10.1080/10485252.2012.752083 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:273-313 Template-Type: ReDIF-Article 1.0 Author-Name: Igor Fedotenkov Author-X-Name-First: Igor Author-X-Name-Last: Fedotenkov Title: A bootstrap method to test for the existence of finite moments Abstract: This paper presents a simple bootstrap test to verify the existence of finite moments. The efficacy of the test relies on the fact that in the absence of a first moment and under certain general conditions, the arithmetic average of a sample grows at a rate greater than the growth rates of the arithmetic averages of the sub-samples. Firstly, we show test consistency analytically. Then, Monte-Carlo simulations are performed to compare our test with the Hill estimator. Journal: Journal of Nonparametric Statistics Pages: 315-322 Issue: 2 Volume: 25 Year: 2013 Month: 6 X-DOI: 10.1080/10485252.2012.752487 File-URL: http://hdl.handle.net/10.1080/10485252.2012.752487 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:315-322 Template-Type: ReDIF-Article 1.0 Author-Name: Georg Ch. Pflug Author-X-Name-First: Georg Ch. Author-X-Name-Last: Pflug Author-Name: Roger J.-B. Wets Author-X-Name-First: Roger J.-B. Author-X-Name-Last: Wets Title: Shape-restricted nonparametric regression with overall noisy measurements Abstract: For a nonparametric regression problem with errors in variables, we consider a shape-restricted regression function estimate, which does not require the choice of bandwidth parameters. We demonstrate that this estimate is consistent for classes of regression function candidates, which are closed under the graph topology. Journal: Journal of Nonparametric Statistics Pages: 323-338 Issue: 2 Volume: 25 Year: 2013 Month: 6 X-DOI: 10.1080/10485252.2012.754890 File-URL: http://hdl.handle.net/10.1080/10485252.2012.754890 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:323-338 Template-Type: ReDIF-Article 1.0 Author-Name: Sherzod M. Mirakhmedov Author-X-Name-First: Sherzod M. Author-X-Name-Last: Mirakhmedov Author-Name: S. Rao Jammalamadaka Author-X-Name-First: S. Rao Author-X-Name-Last: Jammalamadaka Title: Higher-order expansions and efficiencies of tests based on spacings Abstract: Statistics based on spacings, or the gaps between points, have been widely used in many contexts, primarily in testing goodness of fit. This paper derives Edgeworth-type asymptotic expansions for the sum of functions of s-step spacings where s, the order of spacings, may increase together with the sample size n. When s is fixed, it is known that only the Greenwood test, based on the sum of squares of these spacings, is first-order asymptotically efficient. In contrast, it is shown here that if s goes to infinity, there exist many other tests which are first-order efficient. We introduce and study the second-order efficiency of such tests and show that if s is sufficiently large relative to n, the Greenwood test is no longer second-order efficient. Interestingly, we see that the common phenomenon of first-order efficiency implying second-order efficiency does not hold true in this situation. Journal: Journal of Nonparametric Statistics Pages: 339-359 Issue: 2 Volume: 25 Year: 2013 Month: 6 X-DOI: 10.1080/10485252.2012.755530 File-URL: http://hdl.handle.net/10.1080/10485252.2012.755530 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:339-359 Template-Type: ReDIF-Article 1.0 Author-Name: Tang Qingguo Author-X-Name-First: Tang Author-X-Name-Last: Qingguo Title: B-spline estimation for semiparametric varying-coefficient partially linear regression with spatial data Abstract: This paper considers a varying-coefficient partially linear regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the unknown parameters and coefficient functions. Under mild regularity assumptions, the asymptotic distribution of the estimator of the unknown parameter vector is established. The global convergence rates of the B-spline estimators of the unknown coefficient functions are established. The asymptotic distributions of the B-spline estimators of the unknown coefficient functions are also derived. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Boston housing data is used to illustrate our proposed methodology. Journal: Journal of Nonparametric Statistics Pages: 361-378 Issue: 2 Volume: 25 Year: 2013 Month: 6 X-DOI: 10.1080/10485252.2012.758263 File-URL: http://hdl.handle.net/10.1080/10485252.2012.758263 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:361-378 Template-Type: ReDIF-Article 1.0 Author-Name: Hui Zhao Author-X-Name-First: Hui Author-X-Name-Last: Zhao Author-Name: Yang Li Author-X-Name-First: Yang Author-X-Name-Last: Li Author-Name: Jianguo Sun Author-X-Name-First: Jianguo Author-X-Name-Last: Sun Title: Semiparametric analysis of multivariate panel count data with dependent observation processes and a terminal event Abstract: This paper considers regression analysis of multivariate panel count data in the presence of some terminal events. Furthermore, both the observation process and the terminal event may be correlated with the recurrent event process of interest. For the problem, we present a semiparametric additive model for the mean function of the recurrent event process and an estimating equation-based inference procedure is developed for the estimation of regression parameters. In the procedure, the inverse survival probability weighting technique is used and the asymptotic properties of the proposed estimators are established. Extensive simulation studies are conducted to evaluate the finite sample properties of the proposed approach, and the results show that the proposed procedures work well for practical situations. Journal: Journal of Nonparametric Statistics Pages: 379-394 Issue: 2 Volume: 25 Year: 2013 Month: 6 X-DOI: 10.1080/10485252.2012.758724 File-URL: http://hdl.handle.net/10.1080/10485252.2012.758724 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:379-394 Template-Type: ReDIF-Article 1.0 Author-Name: Jiangyan Wang Author-X-Name-First: Jiangyan Author-X-Name-Last: Wang Author-Name: Fuxia Cheng Author-X-Name-First: Fuxia Author-X-Name-Last: Cheng Author-Name: Lijian Yang Author-X-Name-First: Lijian Author-X-Name-Last: Yang Title: Smooth simultaneous confidence bands for cumulative distribution functions Abstract: A plug-in kernel estimator is proposed for Hölder continuous cumulative distribution function (cdf) based on a random sample. Uniform closeness between the proposed estimator and the empirical cdf estimator is established, while the proposed estimator is smooth instead of a step function. A smooth simultaneous confidence band is constructed based on the smooth distribution estimator and the Kolmogorov distribution. Extensive simulation study using two different automatic bandwidths confirms the theoretical findings. Journal: Journal of Nonparametric Statistics Pages: 395-407 Issue: 2 Volume: 25 Year: 2013 Month: 6 X-DOI: 10.1080/10485252.2012.759219 File-URL: http://hdl.handle.net/10.1080/10485252.2012.759219 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:395-407 Template-Type: ReDIF-Article 1.0 Author-Name: Mikhail Langovoy Author-X-Name-First: Mikhail Author-X-Name-Last: Langovoy Author-Name: Olaf Wittich Author-X-Name-First: Olaf Author-X-Name-Last: Wittich Title: Robust nonparametric detection of objects in noisy images Abstract: We propose a novel statistical hypothesis testing method for the detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown shapes in the presence of nonparametric noise of unknown level and of unknown distribution. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. We prove results on consistency and algorithmic complexity of our testing procedure. In addition, we address not only an asymptotic behaviour of the method, but also a finite sample performance of our test. Journal: Journal of Nonparametric Statistics Pages: 409-426 Issue: 2 Volume: 25 Year: 2013 Month: 6 X-DOI: 10.1080/10485252.2012.759570 File-URL: http://hdl.handle.net/10.1080/10485252.2012.759570 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:409-426 Template-Type: ReDIF-Article 1.0 Author-Name: Gerrit Eichner Author-X-Name-First: Gerrit Author-X-Name-Last: Eichner Author-Name: Winfried Stute Author-X-Name-First: Winfried Author-X-Name-Last: Stute Title: Rank transformations in Kernel density estimation Abstract: We introduce and study a kernel density estimator which takes into account not only the local information contained in the data, but also their global structure given through the ranks. The approach allows for an adaptive choice of the smoothing parameters which avoids estimation of higher order derivatives. Our methodology also leads to a new isoperimetric problem which seems to be of independent interest. While in traditional kernel smoothing efficiency is obtained by choosing proper kernels, this role is now played by appropriate rank transformations. Journal: Journal of Nonparametric Statistics Pages: 427-445 Issue: 2 Volume: 25 Year: 2013 Month: 6 X-DOI: 10.1080/10485252.2012.760737 File-URL: http://hdl.handle.net/10.1080/10485252.2012.760737 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:427-445 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Serfling Author-X-Name-First: Robert Author-X-Name-Last: Serfling Author-Name: Satyaki Mazumder Author-X-Name-First: Satyaki Author-X-Name-Last: Mazumder Title: Computationally easy outlier detection via projection pursuit with finitely many directions Abstract: Outlier detection is fundamental to data analysis. Desirable properties are affine invariance, robustness, low computational burden, and nonimposition of elliptical contours. However, leading methods fail to possess all of these features. The Mahalanobis distance outlyingness (MD) imposes elliptical contours. The projection outlyingness, powerfully involving projections of the data onto all univariate directions, is highly computationally intensive. Computationally easy variants using projection pursuit with but finitely many directions have been introduced, but these fail to capture at once the other desired properties. Here, we develop a 'robust Mahalanobis spatial outlyingness on projections' (RMSP) function, which indeed satisfies all the four desired properties. Pre-transformation to a strong invariant coordinate system yields affine invariance, 'spatial trimming' yields robustness, and 'spatial Mahalanobis outlyingness' is used to obtain computational ease and smooth, unconstrained contours. From empirical study using artificial and actual data, our findings are that SUP is outclassed by MD and RMSP, that MD and RMSP are competitive, and that RMSP is especially advantageous in describing the intermediate outlyingness structure when elliptical contours are not assumed. Journal: Journal of Nonparametric Statistics Pages: 447-461 Issue: 2 Volume: 25 Year: 2013 Month: 6 X-DOI: 10.1080/10485252.2013.766335 File-URL: http://hdl.handle.net/10.1080/10485252.2013.766335 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:447-461 Template-Type: ReDIF-Article 1.0 Author-Name: Yu Ryan Yue Author-X-Name-First: Yu Ryan Author-X-Name-Last: Yue Author-Name: Ji Meng Loh Author-X-Name-First: Ji Meng Author-X-Name-Last: Loh Title: Bayesian nonparametric estimation of pair correlation function for inhomogeneous spatial point processes Abstract: The pair correlation function (PCF) is a useful tool for studying spatial point patterns. It is often estimated by some nonparametric approach such as kernel smoothing. However, the statistical properties of the kernel estimator are highly dependent on the choice of bandwidth. An inappropriate value of the bandwidth may lead to an estimator with a large bias or variance or both. In this work, we present an alternative PCF estimator based on Bayesian nonparametric regression. The method provides data-driven smoothing and intuitive uncertainty measures, together with efficient computation. The merits of our method are demonstrated via a simulation study and a couple of applications involving astronomy data and data on restaurant locations. Journal: Journal of Nonparametric Statistics Pages: 463-474 Issue: 2 Volume: 25 Year: 2013 Month: 6 X-DOI: 10.1080/10485252.2013.767337 File-URL: http://hdl.handle.net/10.1080/10485252.2013.767337 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:463-474 Template-Type: ReDIF-Article 1.0 Author-Name: Heng Peng Author-X-Name-First: Heng Author-X-Name-Last: Peng Author-Name: Hongjia Yan Author-X-Name-First: Hongjia Author-X-Name-Last: Yan Author-Name: Wenyang Zhang Author-X-Name-First: Wenyang Author-X-Name-Last: Zhang Title: The connection between cross-validation and Akaike information criterion in a semiparametric family Abstract: Both Akaike information criterion and cross-validation are important tools in model selection. Stone [(1977), 'An Asymptotic Equivalence of Choice of Model by Cross-Validation and Akaikes Criterion', Journal of the Royal Statistical Society, Series B, 39, 44-47] established the equivalence of these two criteria for parametric models. In this paper, we build a similar equivalence for a large semiparametric family. Journal: Journal of Nonparametric Statistics Pages: 475-485 Issue: 2 Volume: 25 Year: 2013 Month: 6 X-DOI: 10.1080/10485252.2013.767338 File-URL: http://hdl.handle.net/10.1080/10485252.2013.767338 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:475-485 Template-Type: ReDIF-Article 1.0 Author-Name: Hammou El Barmi Author-X-Name-First: Hammou Author-X-Name-Last: El Barmi Author-Name: Lahcen El Bermi Author-X-Name-First: Lahcen Author-X-Name-Last: El Bermi Title: Empirical likelihood ratio test for symmetry against type I bias with applications to competing risks Abstract: A random variable X with cumulative distribution function F is said to have a symmetric distribution about θ if and only if X - θ and - X+θ are identically distributed. Different types of partial skewness and one-sided bias are obtained by looking at different types of orderings between the distributions of X - θ and - X+θ. For example, X, or equivalently F, is said to have type I bias about θ if X - θ is stochastically larger than - X+θ. In this paper, we assume that F is continuous, θ is known and develops an empirical likelihood ratio type test for testing for symmetry about θ against this type of alternative. This test is shown to be asymptotically distribution free and the results of a simulation study show that it outperforms in terms of power, a test developed for the same problem in Alfieri and El Barmi [(2005), 'Nonparametric Estimation of a Distribution Function with Type I Bias with Applications to Competing Risks', Journal of Nonparametric Statistics, 17, 319-333]. It turns out that the results developed here can be extended in a natural way to compare the sub-survival functions corresponding to two risks in a competing risks setting. We show how this can be done and illustrate our theoretical results with a real life example. Journal: Journal of Nonparametric Statistics Pages: 487-498 Issue: 2 Volume: 25 Year: 2013 Month: 6 X-DOI: 10.1080/10485252.2013.772177 File-URL: http://hdl.handle.net/10.1080/10485252.2013.772177 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:487-498 Template-Type: ReDIF-Article 1.0 Author-Name: Houssein I. Assaad Author-X-Name-First: Houssein I. Author-X-Name-Last: Assaad Author-Name: Pankaj K. Choudhary Author-X-Name-First: Pankaj K. Author-X-Name-Last: Choudhary Title: L-statistics for repeated measurements data with application to trimmed means, quantiles and tolerance intervals Abstract: The L-statistics form an important class of estimators in nonparametric statistics. Its members include trimmed means and sample quantiles and functions thereof. This article is devoted to theory and applications of L-statistics for repeated measurements data, wherein the measurements on the same subject are dependent and the measurements from different subjects are independent. This article has three main goals: (a) Show that the L-statistics are asymptotically normal for repeated measurements data. (b) Present three statistical applications of this result, namely, location estimation using trimmed means, quantile estimation and construction of tolerance intervals. (c) Obtain a Bahadur representation for sample quantiles. These results are generalisations of similar results for independently and identically distributed data. The practical usefulness of these results is illustrated by analysing a real data-set involving measurement of systolic blood pressure. The properties of the proposed point and interval estimators are examined via simulation. Journal: Journal of Nonparametric Statistics Pages: 499-521 Issue: 2 Volume: 25 Year: 2013 Month: 6 X-DOI: 10.1080/10485252.2013.772178 File-URL: http://hdl.handle.net/10.1080/10485252.2013.772178 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:499-521 Template-Type: ReDIF-Article 1.0 Author-Name: Riquan Zhang Author-X-Name-First: Riquan Author-X-Name-Last: Zhang Author-Name: Weihua Zhao Author-X-Name-First: Weihua Author-X-Name-Last: Zhao Author-Name: Jicai Liu Author-X-Name-First: Jicai Author-X-Name-Last: Liu Title: Robust estimation and variable selection for semiparametric partially linear varying coefficient model based on modal regression Abstract: The semiparametric partially linear varying coefficient models (SPLVCM) are frequently used in statistical modelling, but most existing methods were built on either the least-square or likelihood-based methods, which are very sensitive to the outliers and their efficiency may be significantly reduced for heavy tail error distribution. This paper proposes a new efficient and robust estimation procedure for the SPLVCM based on modal regression. We establish the asymptotic normality of proposed estimators for both the parametric and nonparametric parts, and show that the estimators achieve the best convergence rate. Moreover, we develop a variable selection procedure to select significant parametric components for the SPLVCM and prove the method possessing the oracle property. We also discuss the bandwidth selection and propose an expectation-maximisation-type algorithm for the proposed estimation procedure. Some simulation results and real data analysis confirm that the newly proposed method works very competitively compared to other existing methods. Journal: Journal of Nonparametric Statistics Pages: 523-544 Issue: 2 Volume: 25 Year: 2013 Month: 6 X-DOI: 10.1080/10485252.2013.772179 File-URL: http://hdl.handle.net/10.1080/10485252.2013.772179 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:523-544 Template-Type: ReDIF-Article 1.0 Author-Name: Olga Y. Savchuk Author-X-Name-First: Olga Y. Author-X-Name-Last: Savchuk Author-Name: Anton Schick Author-X-Name-First: Anton Author-X-Name-Last: Schick Title: Density estimation for power transformations Abstract: Consider a random sample X ₁, ..., X _n from a density f and a positive α. The density g of t(X ₁)=&7CX ₁&7C-super-αsign(X ₁) can be estimated in two ways: by a kernel estimator based on the transformed data t(X ₁), ..., t(X _n) or by a plug-in estimator that replaces in the expression for g the unknown density f by a kernel estimator based on the original data. We compare the performance of these two estimators pointwise using the MSE and globally using the mean integrated squared error. From the pointwise comparison, we found that the plug-in estimator is mostly better in the case α>1 when f is symmetric and unimodal, and in the case α≥2.5 when f is right-skewed and/or bimodal. For α>1, the plug-in estimator performs better around the modes of g, while the transformed data estimator is better in the tails of g. Our global comparison shows that the plug-in estimator has a faster rate of convergence for 0.4≤α>1 and 1>α>2. For α>0.4, the plug-in estimator is preferable for a symmetric density f with exponentially decaying tails, while the transformed data estimator is preferable when f is right-skewed or heavy-tailed. Applications to real and simulated data illustrate our theoretical findings. Journal: Journal of Nonparametric Statistics Pages: 545-559 Issue: 3 Volume: 25 Year: 2013 Month: 9 X-DOI: 10.1080/10485252.2013.811788 File-URL: http://hdl.handle.net/10.1080/10485252.2013.811788 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:3:p:545-559 Template-Type: ReDIF-Article 1.0 Author-Name: Alan Huang Author-X-Name-First: Alan Author-X-Name-Last: Huang Title: Density estimation and nonparametric inferences using maximum likelihood weighted kernels Abstract: We show that maximum likelihood weighted kernel density estimation offers a unified approach to density estimation and nonparametric inferences. For density estimation, the approach is a generalisation of the standard kernel density estimator that allows the weights attached to each kernel to be chosen by maximum likelihood, instead of being set to n -super- - 1 from the outset (see also Jones, M.C., and Henderson, D.A. (2005), 'Maximum Likelihood Kernel Density Estimation', Technical Report 01/05, Department of Statistics, The Open University, UK). For nonparametric inferences, the approach offers a natural, smoothed analogue to empirical likelihood (Owen, A.B. (2001), Empirical Likelihood, Boca Raton, FL: Chapman and Hall/CRC) for inferences on functionals of the underlying distribution, such as its mean or median. Numerical results demonstrate that the proposed method is comparable to the standard kernel density estimator (of the same bandwidth) for density estimation, but can offer noticeable small-sample improvements over empirical likelihood for inferences when the underlying distribution is continuous. Journal: Journal of Nonparametric Statistics Pages: 561-571 Issue: 3 Volume: 25 Year: 2013 Month: 9 X-DOI: 10.1080/10485252.2013.797090 File-URL: http://hdl.handle.net/10.1080/10485252.2013.797090 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:3:p:561-571 Template-Type: ReDIF-Article 1.0 Author-Name: Sébastien Da Veiga Author-X-Name-First: Sébastien Author-X-Name-Last: Da Veiga Author-Name: Fabrice Gamboa Author-X-Name-First: Fabrice Author-X-Name-Last: Gamboa Title: Efficient estimation of sensitivity indices Abstract: In this paper, we address the problem of efficient estimation of Sobol sensitivity indices. First, we focus on general functional integrals of conditional moments of the form 𝔼(ψ(𝔼(ϕ(Y)&7CX))) where (X, Y) is a random vector with joint density f and ψ and ϕ are functions that are differentiable enough. In particular, we show that asymptotical efficient estimation of this functional boils down to the estimation of crossed quadratic functionals. An efficient estimate of first-order sensitivity indices is then derived as a special case. We investigate its properties on several analytical functions and illustrate its interest on a reservoir engineering case. Journal: Journal of Nonparametric Statistics Pages: 573-595 Issue: 3 Volume: 25 Year: 2013 Month: 9 X-DOI: 10.1080/10485252.2013.784762 File-URL: http://hdl.handle.net/10.1080/10485252.2013.784762 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:3:p:573-595 Template-Type: ReDIF-Article 1.0 Author-Name: Demetris Athienitis Author-X-Name-First: Demetris Author-X-Name-Last: Athienitis Author-Name: Ronald Randles Author-X-Name-First: Ronald Author-X-Name-Last: Randles Title: Distortion sensitivity of estimators of location Abstract: Robustness measures and procedures have traditionally been developed and implemented through the contamination model of Hampel et al. [2005, Robust Statistics: The Approach Based on Influence Functions, Wiley Series in Probability and Statistics (Vol. 114), New York: Wiley]. We present a distortion model that takes a symmetric probability density function and skews it infinitesimally in a specific direction thereby distorting every realisation of the distribution, a model based upon the work of Fechner [1897, 'Th.(1897)', in Kollektivmasslehre, Leipzig: Engelman]. Robustness to distortion of a symmetric signal is determined as the rate of change of the functional of an affine-equivariant location estimator under the Fechner model. The mean, median and Hodges-Lehman estimators are compared under this model. Journal: Journal of Nonparametric Statistics Pages: 597-617 Issue: 3 Volume: 25 Year: 2013 Month: 9 X-DOI: 10.1080/10485252.2013.787423 File-URL: http://hdl.handle.net/10.1080/10485252.2013.787423 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:3:p:597-617 Template-Type: ReDIF-Article 1.0 Author-Name: Mohamed Boutahar Author-X-Name-First: Mohamed Author-X-Name-Last: Boutahar Author-Name: Badih Ghattas Author-X-Name-First: Badih Author-X-Name-Last: Ghattas Author-Name: Denys Pommeret Author-X-Name-First: Denys Author-X-Name-Last: Pommeret Title: Nonparametric comparison of several transformations of distribution functions Abstract: This paper considers two random variables such that there exists a monotone transformation between their distribution functions. The problem is to test if there is a change in this transformation when these two variables are observed under K different conditions. The approach considered is a CUSUM test based on the cumulative sum of the residuals and a test statistic is proposed for testing the equality of the K transformations. The asymptotic distribution of the test statistic is derived and its finite sample properties are examined by simulation. As a further illustration, an analysis of a real data set concerning the impact of the financial crisis of September 2008 is given. Journal: Journal of Nonparametric Statistics Pages: 619-633 Issue: 3 Volume: 25 Year: 2013 Month: 9 X-DOI: 10.1080/10485252.2013.799158 File-URL: http://hdl.handle.net/10.1080/10485252.2013.799158 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:3:p:619-633 Template-Type: ReDIF-Article 1.0 Author-Name: Tarn Duong Author-X-Name-First: Tarn Author-X-Name-Last: Duong Title: Local significant differences from nonparametric two-sample tests Abstract: We establish a framework to investigate the local differences of two multivariate data samples, as measured by a statistically significant two-sample test. This framework identifies the locally significant difference regions by computing local test statistics based on the squared difference of two kernel density estimators. The key differences between the data samples are concentrated in these significantly different regions. We illustrate the visualisation and interpretation of local significant differences for simulated data, and their potential in the role of biomarker discovery for biological/biomedical data. Journal: Journal of Nonparametric Statistics Pages: 635-645 Issue: 3 Volume: 25 Year: 2013 Month: 9 X-DOI: 10.1080/10485252.2013.810217 File-URL: http://hdl.handle.net/10.1080/10485252.2013.810217 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:3:p:635-645 Template-Type: ReDIF-Article 1.0 Author-Name: Xiaolin Chen Author-X-Name-First: Xiaolin Author-X-Name-Last: Chen Author-Name: Qihua Wang Author-X-Name-First: Qihua Author-X-Name-Last: Wang Title: Semiparametric proportional mean residual life model with covariates missing at random Abstract: In this paper, we consider statistical inference for the proportional mean residual life model when some covariates are missing at random. Simple and augmented inverse probability-weighted estimating equations are used to obtain the estimators of the regression coefficients and baseline mean residual life function. The unknown non-missingness probability and some unknown conditional expectations are estimated by the kernel smoothing technique. We show that the simple inverse probability-weighted estimator with estimated non-missingness probability is more efficient than that with the true non-missingness probability, while the augmented inverse probability-weighted estimator with estimated non-missingness probability and that with the true non-missingness probability have the same efficiency. The asymptotic properties of all the proposed estimators are established. Extensive simulation studies are conducted to examine the finite sample performance of the proposed estimator. At last, the proposed method is applied to the mouse leukaemia data. Journal: Journal of Nonparametric Statistics Pages: 647-663 Issue: 3 Volume: 25 Year: 2013 Month: 9 X-DOI: 10.1080/10485252.2013.779376 File-URL: http://hdl.handle.net/10.1080/10485252.2013.779376 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:3:p:647-663 Template-Type: ReDIF-Article 1.0 Author-Name: Justin Chown Author-X-Name-First: Justin Author-X-Name-Last: Chown Author-Name: Ursula U. Müller Author-X-Name-First: Ursula U. Author-X-Name-Last: Müller Title: Efficiently estimating the error distribution in nonparametric regression with responses missing at random Abstract: This article considers nonparametric regression models with multivariate covariates and with responses missing at random. We estimate the regression function with a local polynomial smoother. The residual-based empirical distribution function that only uses complete cases, i.e. residuals that can actually be constructed from the data, is shown to be efficient in the sense of Hájek and Le Cam. In the proofs we derive, more generally, the efficient influence function for estimating an arbitrary linear functional of the error distribution; this covers the distribution function as a special case. We also show that the complete case residual-based empirical distribution function admits a functional central limit theorem. This is done by applying the transfer principle for complete case statistics developed by Koul et al. [(2012), 'The Transfer Principle: a Tool for Complete Case Analysis', Annals of Statistics, 40, 3031-3049], which makes it possible to adapt known results for fully observed data to the missing data case. The article concludes with a small simulation study investigating the performance of the complete case residual-based empirical distribution function. Journal: Journal of Nonparametric Statistics Pages: 665-677 Issue: 3 Volume: 25 Year: 2013 Month: 9 X-DOI: 10.1080/10485252.2013.795222 File-URL: http://hdl.handle.net/10.1080/10485252.2013.795222 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:3:p:665-677 Template-Type: ReDIF-Article 1.0 Author-Name: Yichen Gao Author-X-Name-First: Yichen Author-X-Name-Last: Gao Author-Name: Kunpeng Li Author-X-Name-First: Kunpeng Author-X-Name-Last: Li Title: Nonparametric estimation of fixed effects panel data models Abstract: In this paper, we consider the problem of estimating a nonparametric panel data models with fixed effects. We propose using the profile least-squares method to concentrate out the fixed effects and then estimate the unknown function by the kernel method. We show that our proposed estimator is consistent and has an asymptotically normal distribution. Monte Carlo simulations show that our proposed estimator performs well compared with several existing estimators. Journal: Journal of Nonparametric Statistics Pages: 679-693 Issue: 3 Volume: 25 Year: 2013 Month: 9 X-DOI: 10.1080/10485252.2013.808744 File-URL: http://hdl.handle.net/10.1080/10485252.2013.808744 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:3:p:679-693 Template-Type: ReDIF-Article 1.0 Author-Name: Francisco Cuevas Author-X-Name-First: Francisco Author-X-Name-Last: Cuevas Author-Name: Emilio Porcu Author-X-Name-First: Emilio Author-X-Name-Last: Porcu Author-Name: Ronny Vallejos Author-X-Name-First: Ronny Author-X-Name-Last: Vallejos Title: Study of spatial relationships between two sets of variables: a nonparametric approach Abstract: We propose a new method for estimating a codispersion coefficient to quantify the association between two spatial variables. Our proposal is based on a Nadaraya-Watson version of the codispersion coefficient through a suitable kernel. Under regularity conditions, we derive expressions for the bias and mean square error for a kernel version of the cross-variogram and establish the consistency of a Nadaraya-Watson estimator of the codispersion coefficient. In addition, we propose a bandwidth selection method for both the variogram and the cross-variogram. Monte Carlo simulations support the theoretical findings, and as a result, the new proposal performs better than the classic Matheron's estimator. The proposed method is useful for quantifying spatial associations between two variables measured at the same location. Finally, we study forest data concerning the relationship among the tree height, basal area, elevation and slope of Pinus radiata plantations. A two-dimensional codispersion map is constructed to provide insight into the spatial association between these variables. Journal: Journal of Nonparametric Statistics Pages: 695-714 Issue: 3 Volume: 25 Year: 2013 Month: 9 X-DOI: 10.1080/10485252.2013.797091 File-URL: http://hdl.handle.net/10.1080/10485252.2013.797091 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:3:p:695-714 Template-Type: ReDIF-Article 1.0 Author-Name: Mary C. Meyer Author-X-Name-First: Mary C. Author-X-Name-Last: Meyer Title: Semi-parametric additive constrained regression Abstract: The additive isotonic least-squares regression model has been fit using a sequential pooled adjacent violators algorithm, estimating each isotonic component in turn, and looping until convergence. However, the individual components are not, in general, estimable. The sum of the components, i.e. the expected value of the response, has a unique estimate, which can be found using a single cone projection. Estimators for the individual components are then easily obtained, which are unique if the conditions for estimability hold. Parametrically modelled covariates are easily included in the cone projection specification. The cone structure also provides information about the degrees of freedom of the fit, which can be used in inference methods, variable selection, and estimation of the model variance. Simulations show that these methods can compare favourably to standard parametric methods, even when the parametric assumptions are correct. The estimation and inference methods can be extended to other constraints such as convex regression or isotonic regression on partial orderings. Journal: Journal of Nonparametric Statistics Pages: 715-730 Issue: 3 Volume: 25 Year: 2013 Month: 9 X-DOI: 10.1080/10485252.2013.797577 File-URL: http://hdl.handle.net/10.1080/10485252.2013.797577 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:3:p:715-730 Template-Type: ReDIF-Article 1.0 Author-Name: Jinfeng Xu Author-X-Name-First: Jinfeng Author-X-Name-Last: Xu Title: Resampling-based efficient shrinkage method for non-smooth minimands Abstract: In many regression models, the coefficients are typically estimated by optimising an objective function with a U-statistic structure. Under such a setting, we propose a simple and general method for simultaneous coefficient estimation and variable selection. It combines an efficient quadratic approximation of the objective function with the adaptive lasso penalty to yield a piecewise-linear regularisation path which can be easily obtained from the fast lars-lasso algorithm. Furthermore, the standard asymptotic oracle properties can be established under general conditions without requiring the covariance assumption (Wang, H., and Leng, C. (2007), 'Unified Lasso Estimation by Least Squares Approximation', Journal of the American Statistical Association, 102, 1039-1048). This approach applies to many semiparametric regression problems. Three examples are used to illustrate the practical utility of our proposal. Numerical results based on simulated and real data are provided. Journal: Journal of Nonparametric Statistics Pages: 731-743 Issue: 3 Volume: 25 Year: 2013 Month: 9 X-DOI: 10.1080/10485252.2013.797977 File-URL: http://hdl.handle.net/10.1080/10485252.2013.797977 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:3:p:731-743 Template-Type: ReDIF-Article 1.0 Author-Name: K. S. McConville Author-X-Name-First: K. S. Author-X-Name-Last: McConville Author-Name: F. J. Breidt Author-X-Name-First: F. J. Author-X-Name-Last: Breidt Title: Survey design asymptotics for the model-assisted penalised spline regression estimator Abstract: The total of a study variable in a finite population may be estimated using data from a complex survey via Horvitz-Thompson estimation. If additional auxiliary information is available, then efficiency is often improved via model-assisted survey regression estimation. Semiparametric models based on penalised spline regression are particularly attractive in this context, as they lead to natural extensions of classical survey regression estimators. Existing theory for the model-assisted penalised spline regression estimator does not account for the setting in which the number of knots is large relative to sample size. This gap is addressed by considering survey design asymptotics for the model-assisted penalised spline survey regression estimator, as the finite population size, sample size, and number of knots all increase to infinity. Conditions on the sequence of designs are developed under which the estimator is consistent for the finite population total and its variance is consistently estimated. Journal: Journal of Nonparametric Statistics Pages: 745-763 Issue: 3 Volume: 25 Year: 2013 Month: 9 X-DOI: 10.1080/10485252.2013.780057 File-URL: http://hdl.handle.net/10.1080/10485252.2013.780057 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:3:p:745-763 Template-Type: ReDIF-Article 1.0 Author-Name: Patricia Menéndez Author-X-Name-First: Patricia Author-X-Name-Last: Menéndez Author-Name: Sucharita Ghosh Author-X-Name-First: Sucharita Author-X-Name-Last: Ghosh Author-Name: Hans R. Künsch Author-X-Name-First: Hans R. Author-X-Name-Last: Künsch Author-Name: Willy Tinner Author-X-Name-First: Willy Author-X-Name-Last: Tinner Title: On trend estimation under monotone Gaussian subordination with long-memory: application to fossil pollen series Abstract: Fossil pollen data from stratigraphic cores are irregularly spaced in time due to non-linear age-depth relations. Moreover, their marginal distributions may vary over time. We address these features in a nonparametric regression model with errors that are monotone transformations of a latent continuous-time Gaussian process Z(T). Although Z(T) is unobserved, due to monotonicity, under suitable regularity conditions, it can be recovered facilitating further computations such as estimation of the long-memory parameter and the Hermite coefficients. The estimation of Z(T) itself involves estimation of the marginal distribution function of the regression errors. These issues are considered in proposing a plug-in algorithm for optimal bandwidth selection and construction of confidence bands for the trend function. Some high-resolution time series of pollen records from Lago di Origlio in Switzerland, which go back ca. 20,000 years are used to illustrate the methods. Journal: Journal of Nonparametric Statistics Pages: 765-785 Issue: 4 Volume: 25 Year: 2013 Month: 12 X-DOI: 10.1080/10485252.2013.826357 File-URL: http://hdl.handle.net/10.1080/10485252.2013.826357 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:4:p:765-785 Template-Type: ReDIF-Article 1.0 Author-Name: Lei Yang Author-X-Name-First: Lei Author-X-Name-Last: Yang Author-Name: Xianyi Wu Author-X-Name-First: Xianyi Author-X-Name-Last: Wu Title: Estimation of Dirichlet process priors with monotone missing data Abstract: This article investigates the estimation of Dirichlet process priors DP(α, α¯) of a random (J+1)-dimensional distribution by monotone missing observations, where the precision parameter α is a positive scalar and α¯ a probability measure on ℝ-super-J+1. While α is estimated by maximising a particularly designed likelihood function, α¯ is estimated using kernel smoothing. The asymptotic properties show that the estimate of α is strongly consistent and asymptotically normally distributed. For the estimate of α¯, the L₁ consistency and the optimal bandwidths under an asymptotic mean integrated squared error criterion are examined. Finally, the performance of these estimates are analysed by means of a small simulation. Journal: Journal of Nonparametric Statistics Pages: 787-807 Issue: 4 Volume: 25 Year: 2013 Month: 12 X-DOI: 10.1080/10485252.2013.804074 File-URL: http://hdl.handle.net/10.1080/10485252.2013.804074 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:4:p:787-807 Template-Type: ReDIF-Article 1.0 Author-Name: Huan Wang Author-X-Name-First: Huan Author-X-Name-Last: Wang Author-Name: Mary C. Meyer Author-X-Name-First: Mary C. Author-X-Name-Last: Meyer Author-Name: Jean D. Opsomer Author-X-Name-First: Jean D. Author-X-Name-Last: Opsomer Title: Constrained spline regression in the presence of AR(p) errors Abstract: Extracting the trend from the pattern of observations is always difficult, especially when the trend is obscured by correlated errors. Often, prior knowledge of the trend does not include a parametric family, and instead the valid assumptions are vague, such as 'smooth' or 'monotone increasing'. Incorrectly specifying the trend as some simple parametric form can lead to overestimation of the correlation. The proposed method uses spline regression with shape constraints, such as monotonicity or convexity, for estimation and inference in the presence of stationary AR(p) errors. Standard criteria for selection of penalty parameter, such as Akaike information criterion (AIC), cross-validation and generalised cross-validation, have been shown to behave badly when the errors are correlated and in the absence of shape constraints. In this article, correlation structure and penalty parameter are selected simultaneously using a correlation-adjusted AIC. The asymptotic properties of unpenalised spline regression in the presence of correlation are investigated. It is proved that even if the estimation of the correlation is inconsistent, the corresponding projection estimation of the regression function can still be consistent and have the optimal asymptotic rate, under appropriate conditions. The constrained spline fit attains the convergence rate of unconstrained spline fit in the presence of AR(p) errors. Simulation results show that the constrained estimator typically behaves better than the unconstrained version if the true trend satisfies the constraints. Journal: Journal of Nonparametric Statistics Pages: 809-827 Issue: 4 Volume: 25 Year: 2013 Month: 12 X-DOI: 10.1080/10485252.2013.804075 File-URL: http://hdl.handle.net/10.1080/10485252.2013.804075 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:4:p:809-827 Template-Type: ReDIF-Article 1.0 Author-Name: Hira L. Koul Author-X-Name-First: Hira L. Author-X-Name-Last: Koul Author-Name: Weixing Song Author-X-Name-First: Weixing Author-X-Name-Last: Song Title: Large sample results for varying kernel regression estimates Abstract: The varying kernel density estimates are particularly designed for positive random variables. Unlike the commonly used symmetric kernel density estimates, the varying kernel density estimates do not suffer from the boundary problem. This paper establishes asymptotic normality and uniform almost sure convergence results for a varying kernel density estimate when the underlying random variable is positive. Similar results are also obtained for a varying kernel nonparametric estimate of the regression function when the covariate is positive. Pros and cons of the varying kernel regression estimate are also discussed via a simulation study. Journal: Journal of Nonparametric Statistics Pages: 829-853 Issue: 4 Volume: 25 Year: 2013 Month: 12 X-DOI: 10.1080/10485252.2013.810742 File-URL: http://hdl.handle.net/10.1080/10485252.2013.810742 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:4:p:829-853 Template-Type: ReDIF-Article 1.0 Author-Name: Qi Zheng Author-X-Name-First: Qi Author-X-Name-Last: Zheng Author-Name: Colin Gallagher Author-X-Name-First: Colin Author-X-Name-Last: Gallagher Author-Name: K.B. Kulasekera Author-X-Name-First: K.B. Author-X-Name-Last: Kulasekera Title: Adaptively weighted kernel regression Abstract: We develop a new kernel-based local polynomial methodology for nonparametric regression based on optimising a linear combination of several loss functions. Optimal weights for least squares and quantile loss functions can be chosen to provide maximum efficiency and these optimal weights can be estimated from data. The resulting estimators are at least as efficient as those provided by existing procedures, but can be much more efficient for many distributions. The data-based weights adapt to the tails of the error distribution resulting in a procedure which is both robust and resistant. Furthermore, the assumption of homogeneous error variance is not required. To illustrate its practical use, we apply the proposed method to model the motorcycle data. Journal: Journal of Nonparametric Statistics Pages: 855-872 Issue: 4 Volume: 25 Year: 2013 Month: 12 X-DOI: 10.1080/10485252.2013.813511 File-URL: http://hdl.handle.net/10.1080/10485252.2013.813511 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:4:p:855-872 Template-Type: ReDIF-Article 1.0 Author-Name: Cyrille Joutard Author-X-Name-First: Cyrille Author-X-Name-Last: Joutard Title: Large deviation approximations for the Mann-Whitney statistic and the Jonckheere-Terpstra statistic Abstract: We establish strong large deviation results for the Mann-Whitney statistic and the Jonckheere-Terpstra statistic, that is, asymptotic expansions of large deviation type for the tail probabilities. We then carry out some numerical comparisons with the exact upper tail probabilities for the Wilcoxon-Mann-Whitney test and the Jonckheere-Terpstra test. Journal: Journal of Nonparametric Statistics Pages: 873-888 Issue: 4 Volume: 25 Year: 2013 Month: 12 X-DOI: 10.1080/10485252.2013.816701 File-URL: http://hdl.handle.net/10.1080/10485252.2013.816701 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:4:p:873-888 Template-Type: ReDIF-Article 1.0 Author-Name: Olga Y. Savchuk Author-X-Name-First: Olga Y. Author-X-Name-Last: Savchuk Author-Name: Jeffrey D. Hart Author-X-Name-First: Jeffrey D. Author-X-Name-Last: Hart Author-Name: Simon P. Sheather Author-X-Name-First: Simon P. Author-X-Name-Last: Sheather Title: One-sided cross-validation for nonsmooth regression functions Abstract: The one-sided cross-validation (OSCV) method is shown to be robust to lack of smoothness in the regression function. Two corrections for the case where the regression function has a discontinuous first derivative are proposed. Simulation results suggest that proposed modifications of the OSCV method are efficient for regression functions whose first derivative is discontinuous at more than two points. The OSCV method and its modification outperform the cross-validation method and the Ruppert-Sheather-Wand plug-in method in a data example involving a function that, potentially, has one discontinuity in its derivative. Journal: Journal of Nonparametric Statistics Pages: 889-904 Issue: 4 Volume: 25 Year: 2013 Month: 12 X-DOI: 10.1080/10485252.2013.817575 File-URL: http://hdl.handle.net/10.1080/10485252.2013.817575 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:4:p:889-904 Template-Type: ReDIF-Article 1.0 Author-Name: Minggen Lu Author-X-Name-First: Minggen Author-X-Name-Last: Lu Author-Name: Dana Loomis Author-X-Name-First: Dana Author-X-Name-Last: Loomis Title: Spline-based semiparametric estimation of partially linear Poisson regression with single-index models Abstract: Epidemiological studies have shown that the high levels of air pollution are associated with the increased mortality. To further characterise the health effects of air pollutants, we propose a spline-based partially linear Poisson single-index model to study the relationship of multi-dimensional air pollution exposure to mortality. B-splines are used to approximate the unknown regression function. A modified Fisher scoring method is applied to simultaneously estimate the linear coefficients and the regression function. The estimator of the regression function is consistent with a better than cubic root convergence rate and the estimators of regression parameters are asymptotically normal and efficient. Also a simple and consistent variance estimation approach based on least-squares method is proposed. An extensive Monte Carlo study is conducted to evaluate the finite sample performance of the proposed spline approach. The method is illustrated using data from an epidemiological study of ambient fine particles. Journal: Journal of Nonparametric Statistics Pages: 905-922 Issue: 4 Volume: 25 Year: 2013 Month: 12 X-DOI: 10.1080/10485252.2013.817576 File-URL: http://hdl.handle.net/10.1080/10485252.2013.817576 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:4:p:905-922 Template-Type: ReDIF-Article 1.0 Author-Name: Gang Shen Author-X-Name-First: Gang Author-X-Name-Last: Shen Author-Name: Hui Xu Author-X-Name-First: Hui Author-X-Name-Last: Xu Title: On the isotonic change-point problem Abstract: This work provides a new nonparametric test with a flavour of the classical Mann-Whitney test for the isotonic change-point problem on correlated data with short-range dependence. The test statistic has a normal null limiting distribution and asymptotic test power 1 under the local alternative. Numerical study indicates that it has a similar or slightly better performance than the oracle form of the existing tests on independent data and works very well on moderate-sized correlated data where the existing tests usually fail. Its application to the global temperature data is presented. Journal: Journal of Nonparametric Statistics Pages: 923-937 Issue: 4 Volume: 25 Year: 2013 Month: 12 X-DOI: 10.1080/10485252.2013.821472 File-URL: http://hdl.handle.net/10.1080/10485252.2013.821472 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:4:p:923-937 Template-Type: ReDIF-Article 1.0 Author-Name: Cécile Durot Author-X-Name-First: Cécile Author-X-Name-Last: Durot Author-Name: Piet Groeneboom Author-X-Name-First: Piet Author-X-Name-Last: Groeneboom Author-Name: Hendrik P. Lopuhaä Author-X-Name-First: Hendrik P. Author-X-Name-Last: Lopuhaä Title: Testing equality of functions under monotonicity constraints Abstract: We consider the problem of testing equality of functions f_j:[a, b]→ℝ for j=1, 2, ..., J on the basis of J independent samples from possibly different distributions under the assumption that the functions are monotone. We provide a uniform approach that covers testing equality of monotone regression curves, equality of monotone densities and equality of monotone hazards in the random censorship model. Two test statistics are proposed based on L₁-distances. We show that both statistics are asymptotically normal and we provide bootstrap implementations, which are shown to have critical regions with asymptotic level α. Journal: Journal of Nonparametric Statistics Pages: 939-970 Issue: 4 Volume: 25 Year: 2013 Month: 12 X-DOI: 10.1080/10485252.2013.826356 File-URL: http://hdl.handle.net/10.1080/10485252.2013.826356 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:25:y:2013:i:4:p:939-970 Template-Type: ReDIF-Article 1.0 Author-Name: A. Pepelyshev Author-X-Name-First: A. Author-X-Name-Last: Pepelyshev Author-Name: E. Rafajłowicz Author-X-Name-First: E. Author-X-Name-Last: Rafajłowicz Author-Name: A. Steland Author-X-Name-First: A. Author-X-Name-Last: Steland Title: Estimation of the quantile function using Bernstein-Durrmeyer polynomials Abstract: This paper studies quantile estimation using Bernstein-Durrmeyer polynomials in terms of its mean squared error and integrated mean squared error including rates of convergence as well as its asymptotic distribution. Whereas the rates of convergence are achieved for i.i.d. samples, we also show that the consistency more or less directly follows from the consistency of the sample quantiles, such that our proposal can also be applied for risk measurement in finance and insurance. Furthermore, an improved estimator based on an error-correction approach is proposed for which a general consistency result is established. A crucial issue is how to select the degree of Bernstein-Durrmeyer polynomials. We propose a novel data-adaptive approach that controls the number of modes of the corresponding density estimator. Its consistency including an uniform error bound as well as its limiting distribution in the sense of a general invariance principle are established. The finite sample properties are investigated by a Monte Carlo study. Finally, the results are illustrated by an application to photovoltaic energy research. Journal: Journal of Nonparametric Statistics Pages: 1-20 Issue: 1 Volume: 26 Year: 2014 Month: 3 X-DOI: 10.1080/10485252.2013.826355 File-URL: http://hdl.handle.net/10.1080/10485252.2013.826355 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:1:p:1-20 Template-Type: ReDIF-Article 1.0 Author-Name: Fadoua Balabdaoui Author-X-Name-First: Fadoua Author-X-Name-Last: Balabdaoui Title: Global convergence of the log-concave MLE when the true distribution is geometric Abstract: Let X₁, ..., X_n be i.i.d. from a discrete probability mass function (pmf) p. In Balabdaoui et al. [(2013), 'Asymptotic Distribution of the Discrete Log-Concave mle and Some Applications', JRSS-B, in press], the pointwise limit distribution of the log-concave maximum-likelihood estimator (MLE) was derived in both the well- and misspecified settings. In the well-specified setting, the geometric distribution was excluded, classified as being degenerate. In this article, we establish the global asymptotic theory of the log-concave MLE of a geometric pmf in all ℓ_q distances for q∈{1, 2, ...}∪{∞}. We also show how these asymptotic results could be used in testing whether a pmf is geometric. Journal: Journal of Nonparametric Statistics Pages: 21-59 Issue: 1 Volume: 26 Year: 2014 Month: 3 X-DOI: 10.1080/10485252.2013.826801 File-URL: http://hdl.handle.net/10.1080/10485252.2013.826801 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:1:p:21-59 Template-Type: ReDIF-Article 1.0 Author-Name: Gaku Igarashi Author-X-Name-First: Gaku Author-X-Name-Last: Igarashi Author-Name: Yoshihide Kakizawa Author-X-Name-First: Yoshihide Author-X-Name-Last: Kakizawa Title: On improving convergence rate of Bernstein polynomial density estimator Abstract: This paper is concerned with the Bernstein estimator [Vitale, R.A. (1975), 'A Bernstein Polynomial Approach to Density Function Estimation', in Statistical Inference and Related Topics, ed. M.L. Puri, 2, New York: Academic Press, pp. 87-99] to estimate a density with support [0, 1]. One of the major contributions of this paper is an application of a multiplicative bias correction [Terrell, G.R., and Scott, D.W. (1980), 'On Improving Convergence Rates for Nonnegative Kernel Density Estimators', The Annals of Statistics, 8, 1160-1163], which was originally developed for the standard kernel estimator. Moreover, the renormalised multiplicative bias corrected Bernstein estimator is studied rigorously. The mean squared error (MSE) in the interior and mean integrated squared error of the resulting bias corrected Bernstein estimators as well as the additive bias corrected Bernstein estimator [Leblanc, A. (2010), 'A Bias-reduced Approach to Density Estimation Using Bernstein Polynomials', Journal of Nonparametric Statistics, 22, 459-475] are shown to be O(n-super- - 8/9) when the underlying density has a fourth-order derivative, where n is the sample size. The condition under which the MSE near the boundary is O(n-super- - 8/9) is also discussed. Finally, numerical studies based on both simulated and real data sets are presented. Journal: Journal of Nonparametric Statistics Pages: 61-84 Issue: 1 Volume: 26 Year: 2014 Month: 3 X-DOI: 10.1080/10485252.2013.827195 File-URL: http://hdl.handle.net/10.1080/10485252.2013.827195 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:1:p:61-84 Template-Type: ReDIF-Article 1.0 Author-Name: J.M. Loubes Author-X-Name-First: J.M. Author-X-Name-Last: Loubes Author-Name: C. Marteau Author-X-Name-First: C. Author-X-Name-Last: Marteau Title: Goodness-of-fit testing strategies from indirect observations Abstract: We consider in this paper a goodness-of-fit testing problem in a density framework. In particular, we deal with an error-in-variables model where each new incoming observation is gathered with a random independent error. It is well known that in such a situation, we are faced with an inverse (deconvolution) problem. Nevertheless, following recent results in the Gaussian white noise model, we prove that using procedures containing a deconvolution step is not always necessary. Journal: Journal of Nonparametric Statistics Pages: 85-99 Issue: 1 Volume: 26 Year: 2014 Month: 3 X-DOI: 10.1080/10485252.2013.827680 File-URL: http://hdl.handle.net/10.1080/10485252.2013.827680 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:1:p:85-99 Template-Type: ReDIF-Article 1.0 Author-Name: Xiaoping Shi Author-X-Name-First: Xiaoping Author-X-Name-Last: Shi Author-Name: Yanyan Liu Author-X-Name-First: Yanyan Author-X-Name-Last: Liu Author-Name: Yuanshan Wu Author-X-Name-First: Yuanshan Author-X-Name-Last: Wu Title: Auxiliary covariate in additive hazards regression for survival data Abstract: We consider the additive hazards regression analysis by utilising auxiliary covariate information to improve the efficiency of the statistical inference when the primary covariate is ascertained only for a randomly selected subsample. We construct a martingale-based estimating equation for the regression parameter and establish the asymptotic consistency and normality of the resultant estimator. Simulation study shows that our proposed method can improve the efficiency compared with the estimator which discards the auxiliary covariate information. A real example is also analysed as an illustration. Journal: Journal of Nonparametric Statistics Pages: 101-113 Issue: 1 Volume: 26 Year: 2014 Month: 3 X-DOI: 10.1080/10485252.2013.834337 File-URL: http://hdl.handle.net/10.1080/10485252.2013.834337 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:1:p:101-113 Template-Type: ReDIF-Article 1.0 Author-Name: Yi-Kuan Tseng Author-X-Name-First: Yi-Kuan Author-X-Name-Last: Tseng Author-Name: Ken-Ning Hsu Author-X-Name-First: Ken-Ning Author-X-Name-Last: Hsu Author-Name: Ya-Fang Yang Author-X-Name-First: Ya-Fang Author-X-Name-Last: Yang Title: A semiparametric extended hazard regression model with time-dependent covariates Abstract: We introduce a general class of semiparametric hazard regression models, called extended hazard (EH) models, that are designed to accommodate various survival schemes with time-dependent covariates. The EH model contains both the Cox model and the accelerated failure time (AFT) model as its subclasses so that we can use this nested structure to perform model selection between the Cox model and the AFT model. A class of estimating equations using counting process and martingale techniques is developed to estimate the regression parameters of the proposed model. The performance of the estimating procedure and the impact of model misspecification are assessed through simulation studies. Two data examples, Stanford heart transplant data and Mediterranean fruit flies, egg-laying data, are used to demonstrate the usefulness of the EH model. Journal: Journal of Nonparametric Statistics Pages: 115-128 Issue: 1 Volume: 26 Year: 2014 Month: 3 X-DOI: 10.1080/10485252.2013.836521 File-URL: http://hdl.handle.net/10.1080/10485252.2013.836521 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:1:p:115-128 Template-Type: ReDIF-Article 1.0 Author-Name: Juan Fernández Sánchez Author-X-Name-First: Juan Author-X-Name-Last: Fernández Sánchez Author-Name: Manuel Úbeda-Flores Author-X-Name-First: Manuel Author-X-Name-Last: Úbeda-Flores Title: Semi-polynomial copulas Abstract: In this paper, we characterise a family of bivariate copulas whose sections between the main diagonal and the border of the unit square are polynomial, generalising several families of copulas, including those with quadratic and cubic sections. We also study a measure of association and the tail dependence for this class, illustrating our results with several examples. Journal: Journal of Nonparametric Statistics Pages: 129-140 Issue: 1 Volume: 26 Year: 2014 Month: 3 X-DOI: 10.1080/10485252.2013.839788 File-URL: http://hdl.handle.net/10.1080/10485252.2013.839788 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:1:p:129-140 Template-Type: ReDIF-Article 1.0 Author-Name: Patrick Saart Author-X-Name-First: Patrick Author-X-Name-Last: Saart Author-Name: Jiti Gao Author-X-Name-First: Jiti Author-X-Name-Last: Gao Author-Name: Nam Hyun Kim Author-X-Name-First: Nam Hyun Author-X-Name-Last: Kim Title: Semiparametric methods in nonlinear time series analysis: a selective review Abstract: Time series analysis is a tremendous research area in statistics and econometrics. In a previous review, the author was able to break down up 15 key areas of research interest in time series analysis. Nonetheless, the aim of the review in this current paper is not to cover a wide range of somewhat unrelated topics on the subject, but the key strategy of the review in this paper is to begin with a core the 'curse of dimensionality' in nonparametric time series analysis, and explore further in a metaphorical domino-effect fashion into other closely related areas in semiparametric methods in nonlinear time series analysis. Journal: Journal of Nonparametric Statistics Pages: 141-169 Issue: 1 Volume: 26 Year: 2014 Month: 3 X-DOI: 10.1080/10485252.2013.840724 File-URL: http://hdl.handle.net/10.1080/10485252.2013.840724 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:1:p:141-169 Template-Type: ReDIF-Article 1.0 Author-Name: Peng Lai Author-X-Name-First: Peng Author-X-Name-Last: Lai Author-Name: Ye Tian Author-X-Name-First: Ye Author-X-Name-Last: Tian Author-Name: Heng Lian Author-X-Name-First: Heng Author-X-Name-Last: Lian Title: Estimation and variable selection for generalised partially linear single-index models Abstract: In this paper, we study the problem of estimation and variable selection for generalised partially linear single-index models based on quasi-likelihood, extending existing studies on variable selection for partially linear single-index models to binary and count responses. To take into account the unit norm constraint of the index parameter, we use the 'delete-one-component' approach. The asymptotic normality of the estimates is demonstrated. Furthermore, the smoothly clipped absolute deviation penalty is added for variable selection of parameters both in the nonparametric part and the parametric part, and the oracle property of the variable selection procedure is shown. Finally, some simulation studies are carried out to illustrate the finite sample performance. Journal: Journal of Nonparametric Statistics Pages: 171-185 Issue: 1 Volume: 26 Year: 2014 Month: 3 X-DOI: 10.1080/10485252.2013.841156 File-URL: http://hdl.handle.net/10.1080/10485252.2013.841156 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:1:p:171-185 Template-Type: ReDIF-Article 1.0 Author-Name: Jing Sun Author-X-Name-First: Jing Author-X-Name-Last: Sun Author-Name: Lu Lin Author-X-Name-First: Lu Author-X-Name-Last: Lin Title: Local rank estimation and related test for varying-coefficient partially linear models Abstract: This paper develops a robust estimation procedure for the varying-coefficient partially linear model via local rank technique. The new procedure provides a highly efficient and robust alternative to the local linear least-squares method. In other words, the proposed method is highly efficient across a wide class of non-normal error distributions and it only loses a small amount of efficiency for normal error. Moreover, a test for the hypothesis of constancy for the nonparametric component is proposed. The test statistic is simple and thus the test procedure can be easily implemented. We conduct Monte Carlo simulation to examine the finite sample performance of the proposed procedures and apply them to analyse the environment data set. Both the theoretical and the numerical results demonstrate that the performance of our approach is at least comparable to those existing competitors. Journal: Journal of Nonparametric Statistics Pages: 187-206 Issue: 1 Volume: 26 Year: 2014 Month: 3 X-DOI: 10.1080/10485252.2013.841910 File-URL: http://hdl.handle.net/10.1080/10485252.2013.841910 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:1:p:187-206 Template-Type: ReDIF-Article 1.0 Author-Name: Juan Carlos Rodríguez Author-X-Name-First: Juan Carlos Author-X-Name-Last: Rodríguez Title: Mean estimation through proportion estimation Abstract: In this work a device which changes the problem of mean estimation into that of proportion estimation is proposed. The device consists of perturbing the observations. The goal of the work is the construction of conservative confidence intervals for means. Three applications are given: (1) proportion estimation in the context of cluster random sampling, (2) differences of proportions of a multinomial population and (3) variance estimation. Journal: Journal of Nonparametric Statistics Pages: 207-217 Issue: 2 Volume: 26 Year: 2014 Month: 6 X-DOI: 10.1080/10485252.2013.852193 File-URL: http://hdl.handle.net/10.1080/10485252.2013.852193 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:2:p:207-217 Template-Type: ReDIF-Article 1.0 Author-Name: R. Hable Author-X-Name-First: R. Author-X-Name-Last: Hable Author-Name: A. Christmann Author-X-Name-First: A. Author-X-Name-Last: Christmann Title: Estimation of scale functions to model heteroscedasticity by regularised kernel-based quantile methods Abstract: A main goal of regression is to derive statistical conclusions on the conditional distribution of the output variable Y given the input values x. Two of the most important characteristics of a single distribution are location and scale. Regularised kernel methods (RKMs) - also called support vector machines in a wide sense - are well established to estimate location functions like the conditional median or the conditional mean. We investigate the estimation of scale functions by RKMs when the conditional median is unknown, too. Estimation of scale functions is important, e.g. to estimate the volatility in finance. We consider the median absolute deviation (MAD) and the interquantile range as measures of scale. Our main result shows the consistency of MAD-type RKMs. Journal: Journal of Nonparametric Statistics Pages: 219-239 Issue: 2 Volume: 26 Year: 2014 Month: 6 X-DOI: 10.1080/10485252.2013.875547 File-URL: http://hdl.handle.net/10.1080/10485252.2013.875547 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:2:p:219-239 Template-Type: ReDIF-Article 1.0 Author-Name: Elena Di Bernardino Author-X-Name-First: Elena Author-X-Name-Last: Di Bernardino Author-Name: Clémentine Prieur Author-X-Name-First: Clémentine Author-X-Name-Last: Prieur Title: Estimation of multivariate conditional-tail-expectation using Kendall's process Abstract: This paper deals with the problem of estimating the multivariate version of the Conditional-Tail-Expectation, proposed by Di Bernardino et al. [(2013), 'Plug-in Estimation of Level Sets in a Non-Compact Setting with Applications in Multivariable Risk Theory', ESAIM: Probability and Statistics, (17), 236-256]. We propose a new nonparametric estimator for this multivariate risk-measure, which is essentially based on Kendall's process [Genest and Rivest, (1993), 'Statistical Inference Procedures for Bivariate Archimedean Copulas', Journal of American Statistical Association, 88(423), 1034-1043]. Using the central limit theorem for Kendall's process, proved by Barbe et al. [(1996), 'On Kendall's Process', Journal of Multivariate Analysis, 58(2), 197-229], we provide a functional central limit theorem for our estimator. We illustrate the practical properties of our nonparametric estimator on simulations and on two real test cases. We also propose a comparison study with the level sets-based estimator introduced in Di Bernardino et al. [(2013), 'Plug-In Estimation of Level Sets in A Non-Compact Setting with Applications in Multivariable Risk Theory', ESAIM: Probability and Statistics, (17), 236-256] and with (semi-)parametric approaches. Journal: Journal of Nonparametric Statistics Pages: 241-267 Issue: 2 Volume: 26 Year: 2014 Month: 6 X-DOI: 10.1080/10485252.2014.889137 File-URL: http://hdl.handle.net/10.1080/10485252.2014.889137 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:2:p:241-267 Template-Type: ReDIF-Article 1.0 Author-Name: Takuma Yoshida Author-X-Name-First: Takuma Author-X-Name-Last: Yoshida Author-Name: Kanta Naito Author-X-Name-First: Kanta Author-X-Name-Last: Naito Title: Asymptotics for penalised splines in generalised additive models Abstract: This paper discusses asymptotic theory for penalised spline estimators in generalised additive models. The purpose of this paper is to establish the asymptotic bias and variance as well as the asymptotic normality of the ridge-corrected penalised spline estimator. Furthermore, the asymptotics for the penalised quasi-likelihood fit in mixed models are also discussed. Journal: Journal of Nonparametric Statistics Pages: 269-289 Issue: 2 Volume: 26 Year: 2014 Month: 6 X-DOI: 10.1080/10485252.2014.899360 File-URL: http://hdl.handle.net/10.1080/10485252.2014.899360 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:2:p:269-289 Template-Type: ReDIF-Article 1.0 Author-Name: Jinsong Chen Author-X-Name-First: Jinsong Author-X-Name-Last: Chen Author-Name: Inyoung Kim Author-X-Name-First: Inyoung Author-X-Name-Last: Kim Author-Name: George R. Terrell Author-X-Name-First: George R. Author-X-Name-Last: Terrell Author-Name: Lei Liu Author-X-Name-First: Lei Author-X-Name-Last: Liu Title: Generalised partial linear single-index mixed models for repeated measures data Abstract: In this paper, we propose generalised partial linear single-index mixed models for analysing repeated measures data. A penalised quasi-likelihood approach using P-spline is used to estimate the nonparametric function, linear parameters, and single-index coefficients. Asymptotic properties of the estimators are developed when the dimension of spline basis grows with increasing sample size. Simulation examples and two applications: the study of health effects of air pollution in North Carolina, and treatment effect of naltrexone on health costs for alcohol-dependent individuals, illustrate the effectiveness of our approach. Journal: Journal of Nonparametric Statistics Pages: 291-303 Issue: 2 Volume: 26 Year: 2014 Month: 6 X-DOI: 10.1080/10485252.2014.891029 File-URL: http://hdl.handle.net/10.1080/10485252.2014.891029 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:2:p:291-303 Template-Type: ReDIF-Article 1.0 Author-Name: K. Żychaluk Author-X-Name-First: K. Author-X-Name-Last: Żychaluk Title: Bootstrap bandwidth selection method for local linear estimator in exponential family models Abstract: Many biological experiments involve data whose distribution belongs to the exponential family. Such data are often analysed using generalised linear models but this method requires specification of the link function which can have strong influence on the resulting estimate. Instead a local method based on quasi-likelihood can be used, but the choice of the smoothing parameter is crucial for its performance. A bootstrap bandwidth selection method is proposed and shown to be consistent. Examples of application to data from biological and psychometric experiments are given. Journal: Journal of Nonparametric Statistics Pages: 305-319 Issue: 2 Volume: 26 Year: 2014 Month: 6 X-DOI: 10.1080/10485252.2014.885023 File-URL: http://hdl.handle.net/10.1080/10485252.2014.885023 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:2:p:305-319 Template-Type: ReDIF-Article 1.0 Author-Name: Xiang Zhang Author-X-Name-First: Xiang Author-X-Name-Last: Zhang Author-Name: Yanbing Zheng Author-X-Name-First: Yanbing Author-X-Name-Last: Zheng Title: Nonparametric Bayesian inference for multivariate density functions using Feller priors Abstract: Multivariate density estimation plays an important role in investigating the mechanism of high-dimensional data. This article describes a nonparametric Bayesian approach to the estimation of multivariate densities. A general procedure is proposed for constructing Feller priors for multivariate densities and their theoretical properties as nonparametric priors are established. A blocked Gibbs sampling algorithm is devised to sample from the posterior of the multivariate density. A simulation study is conducted to evaluate the performance of the procedure. Journal: Journal of Nonparametric Statistics Pages: 321-340 Issue: 2 Volume: 26 Year: 2014 Month: 6 X-DOI: 10.1080/10485252.2014.894512 File-URL: http://hdl.handle.net/10.1080/10485252.2014.894512 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:2:p:321-340 Template-Type: ReDIF-Article 1.0 Author-Name: Luai Al Labadi Author-X-Name-First: Luai Author-X-Name-Last: Al Labadi Author-Name: Mahmoud Zarepour Author-X-Name-First: Mahmoud Author-X-Name-Last: Zarepour Title: Goodness-of-fit tests based on the distance between the Dirichlet process and its base measure Abstract: The Dirichlet process is a fundamental tool in studying Bayesian nonparametric inference. The Dirichlet process has several sum representations, where each one of these representations highlights some aspects of this important process. In this paper, we use the sum representations of the Dirichlet process to derive explicit expressions that are used to calculate Kolmogorov, Lévy, and Cramér-von Mises distances between the Dirichlet process and its base measure. The derived expressions of the distance are used to select a proper value for the concentration parameter of the Dirichlet process. These tools are also used in a goodness-of-fit test. Illustrative examples and simulation results are included. Journal: Journal of Nonparametric Statistics Pages: 341-357 Issue: 2 Volume: 26 Year: 2014 Month: 6 X-DOI: 10.1080/10485252.2013.856431 File-URL: http://hdl.handle.net/10.1080/10485252.2013.856431 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:2:p:341-357 Template-Type: ReDIF-Article 1.0 Author-Name: Jin Lee Author-X-Name-First: Jin Author-X-Name-Last: Lee Title: Nonparametric testing for long-horizon predictability with persistent covariates Abstract: We propose a testing procedure for long-horizon predictability via kernel-based nonparametric estimators of long-run covariances between multiperiod returns and persistent covariates. Asymptotic properties of the proposed tests are studied. As for implementation of the test, sieve bootstrap methods are employed to obtain reasonable approximation to the sample distribution of the test statistics. Monte Carlo simulations are conducted to verify the theoretical conjecture. Empirical analysis, using US monthly data from 1929 to 2011, are presented for testing stock return predictability of some forecasting financial variables. Long-term interest rates, unlike default spreads or price-earning ration, are found to show some forecasting power. Journal: Journal of Nonparametric Statistics Pages: 359-372 Issue: 2 Volume: 26 Year: 2014 Month: 6 X-DOI: 10.1080/10485252.2013.870173 File-URL: http://hdl.handle.net/10.1080/10485252.2013.870173 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:2:p:359-372 Template-Type: ReDIF-Article 1.0 Author-Name: Nikolai Dokuchaev Author-X-Name-First: Nikolai Author-X-Name-Last: Dokuchaev Title: Volatility estimation from short time series of stock prices Abstract: We consider estimation of the historical volatility of stock prices. It is assumed that the stock prices are represented as time series formed as samples of the solution of a stochastic differential equation with random and time-varying parameters; these parameters are not observable directly and have unknown evolution law. The price samples are available with limited frequency only. In this setting, the estimation has to be based on short time series, and the estimation error can be significant. We suggest some supplements to the existing nonparametric methods of volatility estimation. Two modifications of the standard summation formula for the volatility are derived. In addition, a linear transformation eliminating the appreciation rate and preserving the volatility is suggested. Journal: Journal of Nonparametric Statistics Pages: 373-384 Issue: 2 Volume: 26 Year: 2014 Month: 6 X-DOI: 10.1080/10485252.2013.844805 File-URL: http://hdl.handle.net/10.1080/10485252.2013.844805 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:2:p:373-384 Template-Type: ReDIF-Article 1.0 Author-Name: David Källberg Author-X-Name-First: David Author-X-Name-Last: Källberg Author-Name: Nikolaj Leonenko Author-X-Name-First: Nikolaj Author-X-Name-Last: Leonenko Author-Name: Oleg Seleznjev Author-X-Name-First: Oleg Author-X-Name-Last: Seleznjev Title: Statistical estimation of quadratic Rényi entropy for a stationary m-dependent sequence Abstract: The Rényi entropy is a generalisation of the Shannon entropy and is widely used in mathematical statistics and applied sciences for quantifying the uncertainty in a probability distribution. We consider estimation of the quadratic Rényi entropy and related functionals for the marginal distribution of a stationary m-dependent sequence. The U-statistic estimators under study are based on the number of ε-close vector observations in the corresponding sample. A variety of asymptotic properties for these estimators are obtained (e.g. consistency, asymptotic normality, and Poisson convergence). The results can be used in diverse statistical and computer science problems whenever the conventional independence assumption is too strong (e.g. ε-keys in time series databases and distribution identification problems for dependent samples). Journal: Journal of Nonparametric Statistics Pages: 385-411 Issue: 2 Volume: 26 Year: 2014 Month: 6 X-DOI: 10.1080/10485252.2013.854438 File-URL: http://hdl.handle.net/10.1080/10485252.2013.854438 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:2:p:385-411 Template-Type: ReDIF-Article 1.0 Author-Name: Derek S. Young Author-X-Name-First: Derek S. Author-X-Name-Last: Young Author-Name: Thomas Mathew Author-X-Name-First: Thomas Author-X-Name-Last: Mathew Title: Improved nonparametric tolerance intervals based on interpolated and extrapolated order statistics Abstract: The standard approach to construct nonparametric tolerance intervals is to use the appropriate order statistics, provided a minimum sample size requirement is met. However, it is well-known that this traditional approach is conservative with respect to the nominal level. One way to improve the coverage probabilities is to use interpolation. However, the extension to the case of two-sided tolerance intervals, as well as for the case when the minimum sample size requirement is not met, have not been studied. In this paper, an approach using linear interpolation is proposed for improving coverage probabilities for the two-sided setting. In the case when the minimum sample size requirement is not met, coverage probabilities are shown to improve by using linear extrapolation. A discussion about the effect on coverage probabilities and expected lengths when transforming the data is also presented. The applicability of this approach is demonstrated using three real data sets. Journal: Journal of Nonparametric Statistics Pages: 415-432 Issue: 3 Volume: 26 Year: 2014 Month: 9 X-DOI: 10.1080/10485252.2014.906594 File-URL: http://hdl.handle.net/10.1080/10485252.2014.906594 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:3:p:415-432 Template-Type: ReDIF-Article 1.0 Author-Name: Yukun Liu Author-X-Name-First: Yukun Author-X-Name-Last: Liu Author-Name: Jiahua Chen Author-X-Name-First: Jiahua Author-X-Name-Last: Chen Author-Name: Ting Li Author-X-Name-First: Ting Author-X-Name-Last: Li Title: Level-specific correction for nonparametric likelihoods Abstract: The popular empirical likelihood method not only has a convenient chi-square limiting distribution but is also Bartlett correctable, leading to a high-order coverage precision of the resulting confidence regions. Meanwhile, it is one of many nonparametric likelihoods in the Cressie-Read power divergence family. The other likelihoods share many attractive properties but are not Bartlett correctable. In this paper, we develop a new technique to achieve the effect of being Bartlett correctable. Our technique is generally applicable to pivotal quantities with chi-square limiting distributions. Numerical experiments and an example reveal that the method is successful for several important nonparametric likelihoods. Journal: Journal of Nonparametric Statistics Pages: 433-449 Issue: 3 Volume: 26 Year: 2014 Month: 9 X-DOI: 10.1080/10485252.2014.929676 File-URL: http://hdl.handle.net/10.1080/10485252.2014.929676 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:3:p:433-449 Template-Type: ReDIF-Article 1.0 Author-Name: Pierre-Yves Massé Author-X-Name-First: Pierre-Yves Author-X-Name-Last: Massé Author-Name: William Meiniel Author-X-Name-First: William Author-X-Name-Last: Meiniel Title: Adaptive confidence bands in the nonparametric fixed design regression model Abstract: In this note, we consider the problem of the existence of adaptive confidence bands in the fixed design regression model, adapting ideas in Hoffmann and Nickl [(2011), 'On Adaptive Inference and Confidence Bands', Annals of Statistics, 39, 2383-2409] to the present case. In the course of the proof, we show that sup-norm adaptive estimators exist as well in the regression setting. Journal: Journal of Nonparametric Statistics Pages: 451-469 Issue: 3 Volume: 26 Year: 2014 Month: 9 X-DOI: 10.1080/10485252.2014.905688 File-URL: http://hdl.handle.net/10.1080/10485252.2014.905688 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:3:p:451-469 Template-Type: ReDIF-Article 1.0 Author-Name: Aboubacar Amiri Author-X-Name-First: Aboubacar Author-X-Name-Last: Amiri Author-Name: Baba Thiam Author-X-Name-First: Baba Author-X-Name-Last: Thiam Title: Consistency of the recursive nonparametric regression estimation for dependent functional data Abstract: We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the mean quadratic error of the considered class of estimators. Our results are established with rates and asymptotic appear bounds, under strong mixing condition. Finally, the feasibility of the proposed estimator is illustrated throughout an empirical study. Journal: Journal of Nonparametric Statistics Pages: 471-487 Issue: 3 Volume: 26 Year: 2014 Month: 9 X-DOI: 10.1080/10485252.2014.907406 File-URL: http://hdl.handle.net/10.1080/10485252.2014.907406 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:3:p:471-487 Template-Type: ReDIF-Article 1.0 Author-Name: Shujie Ma Author-X-Name-First: Shujie Author-X-Name-Last: Ma Title: A plug-in the number of knots selector for polynomial spline regression Abstract: A plug-in the number of interior knots (NIKs) selector is proposed for polynomial spline estimation in nonparametric regression. The existence and properties of the optimal NIKs for spline regression are established by minimising the weighted mean integrated squared error. We obtain plug-in formulae for the optimal NIKs based on the theoretical results of asymptotic optimality, and develop strategies for choosing the NIKs of the spline estimator. The proposed NIKs selection method is tested on our simulated data with quite satisfactory performance, and is illustrated by analysing a fossil data set. Journal: Journal of Nonparametric Statistics Pages: 489-507 Issue: 3 Volume: 26 Year: 2014 Month: 9 X-DOI: 10.1080/10485252.2014.930143 File-URL: http://hdl.handle.net/10.1080/10485252.2014.930143 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:3:p:489-507 Template-Type: ReDIF-Article 1.0 Author-Name: Tadao Hoshino Author-X-Name-First: Tadao Author-X-Name-Last: Hoshino Title: Quantile regression estimation of partially linear additive models Abstract: In this paper, we consider the estimation of partially linear additive quantile regression models where the conditional quantile function comprises a linear parametric component and a nonparametric additive component. We propose a two-step estimation approach: in the first step, we approximate the conditional quantile function using a series estimation method. In the second step, the nonparametric additive component is recovered using either a local polynomial estimator or a weighted Nadaraya-Watson estimator. Both consistency and asymptotic normality of the proposed estimators are established. Particularly, we show that the first-stage estimator for the finite-dimensional parameters attains the semiparametric efficiency bound under homoskedasticity, and that the second-stage estimators for the nonparametric additive component have an oracle efficiency property. Monte Carlo experiments are conducted to assess the finite sample performance of the proposed estimators. An application to a real data set is also illustrated. Journal: Journal of Nonparametric Statistics Pages: 509-536 Issue: 3 Volume: 26 Year: 2014 Month: 9 X-DOI: 10.1080/10485252.2014.929675 File-URL: http://hdl.handle.net/10.1080/10485252.2014.929675 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:3:p:509-536 Template-Type: ReDIF-Article 1.0 Author-Name: Youming Liu Author-X-Name-First: Youming Author-X-Name-Last: Liu Author-Name: Junlian Xu Author-X-Name-First: Junlian Author-X-Name-Last: Xu Title: Wavelet density estimation for negatively associated stratified size-biased sample Abstract: This paper provides upper bounds of wavelet estimations on L-super-p (1≤p>∞) risk for a density function in Besov spaces based on negatively associated stratified size-biased random samples. It turns out that the classical theorem of Donoho, Johnstone, Kerkyacharian and Picard is completely extended to more general cases. More precisely, we consider the model with multiplication noise and allow the sample negatively associated. Our theory is illustrated with a simulation study. Journal: Journal of Nonparametric Statistics Pages: 537-554 Issue: 3 Volume: 26 Year: 2014 Month: 9 X-DOI: 10.1080/10485252.2014.930142 File-URL: http://hdl.handle.net/10.1080/10485252.2014.930142 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:3:p:537-554 Template-Type: ReDIF-Article 1.0 Author-Name: Sam Efromovich Author-X-Name-First: Sam Author-X-Name-Last: Efromovich Title: On shrinking minimax convergence in nonparametric statistics Abstract: ... if we are prepared to assume that the unknown density has k derivatives, then ... the optimal mean integrated squared error is of order n-super- - 2 k/(2 k+1) ... ' The citation is from Silverman [(1986), Density Estimation for Statistics and Data Analysis, London: Chapman & Hall] and its assertion is based on a classical minimax lower bound which is the pillar of the modern nonparametric statistics. This paper proposes a new minimax methodology that implies a faster decreasing minimax lower bound that is attainable by a data-driven estimator, and the same estimator is also minimax under the classical approach. The recommendation is to test performance of estimators via the new and classical minimax approaches. Journal: Journal of Nonparametric Statistics Pages: 555-573 Issue: 3 Volume: 26 Year: 2014 Month: 9 X-DOI: 10.1080/10485252.2014.931394 File-URL: http://hdl.handle.net/10.1080/10485252.2014.931394 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:3:p:555-573 Template-Type: ReDIF-Article 1.0 Author-Name: A.K.M. Fazlur Rahman Author-X-Name-First: A.K.M. Fazlur Author-X-Name-Last: Rahman Author-Name: James D. Lynch Author-X-Name-First: James D. Author-X-Name-Last: Lynch Author-Name: Edsel A. Peña Author-X-Name-First: Edsel A. Author-X-Name-Last: Peña Title: Nonparametric Bayes estimation of gap-time distribution with recurrent event data Abstract: Nonparametric Bayes (NPB) estimation of the gap-time survivor function governing the time to occurrence of a recurrent event in the presence of censoring is considered. In our Bayesian approach, the gap-time distribution, denoted by F, has a Dirichlet process prior with parameter α. We derive NPB and nonparametric empirical Bayes (NPEB) estimators of the survivor function F̄=1 - F and construct point-wise credible intervals. The resulting Bayes estimator of F̄ extends that based on single-event right-censored data, and the PL-type estimator is a limiting case of this Bayes estimator. Through simulation studies, we demonstrate that the PL-type estimator has smaller biases but higher root-mean-squared errors (RMSEs) than those of the NPB and the NPEB estimators. Even in the case of a mis-specified prior measure parameter α, the NPB and the NPEB estimators have smaller RMSEs than the PL-type estimator, indicating robustness of the NPB and NPEB estimators. In addition, the NPB and NPEB estimators are smoother (in some sense) than the PL-type estimator. Journal: Journal of Nonparametric Statistics Pages: 575-598 Issue: 3 Volume: 26 Year: 2014 Month: 9 X-DOI: 10.1080/10485252.2014.906744 File-URL: http://hdl.handle.net/10.1080/10485252.2014.906744 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:3:p:575-598 Template-Type: ReDIF-Article 1.0 Author-Name: Han Lin Shang Author-X-Name-First: Han Lin Author-X-Name-Last: Shang Title: Bayesian bandwidth estimation for a functional nonparametric regression model with mixed types of regressors and unknown error density Abstract: We investigate the issue of bandwidth estimation in a functional nonparametric regression model with function-valued, continuous real-valued and discrete-valued regressors under the framework of unknown error density. Extending from the recent work of Shang (2013) ['Bayesian Bandwidth Estimation for a Nonparametric Functional Regression Model with Unknown Error Density', Computational Statistics & Data Analysis, 67, 185-198], we approximate the unknown error density by a kernel density estimator of residuals, where the regression function is estimated by the functional Nadaraya-Watson estimator that admits mixed types of regressors. We derive a likelihood and posterior density for the bandwidth parameters under the kernel-form error density, and put forward a Bayesian bandwidth estimation approach that can simultaneously estimate the bandwidths. Simulation studies demonstrated the estimation accuracy of the regression function and error density for the proposed Bayesian approach. Illustrated by a spectroscopy data set in the food quality control, we applied the proposed Bayesian approach to select the optimal bandwidths in a functional nonparametric regression model with mixed types of regressors. Journal: Journal of Nonparametric Statistics Pages: 599-615 Issue: 3 Volume: 26 Year: 2014 Month: 9 X-DOI: 10.1080/10485252.2014.916806 File-URL: http://hdl.handle.net/10.1080/10485252.2014.916806 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:3:p:599-615 Template-Type: ReDIF-Article 1.0 Author-Name: Camila P. E. de Souza Author-X-Name-First: Camila P. E. Author-X-Name-Last: de Souza Author-Name: Nancy E. Heckman Author-X-Name-First: Nancy E. Author-X-Name-Last: Heckman Title: Switching nonparametric regression models Abstract: We propose a methodology to analyse data arising from a curve that, over its domain, switches among J states. We consider a sequence of response variables, where each response y depends on a covariate x according to an unobserved state z. The states form a stochastic process and their possible values are j=1, ... , J. If z equals j the expected response of y is one of J unknown smooth functions evaluated at x. We call this model a switching nonparametric regression model. We develop an Expectation-Maximisation algorithm to estimate the parameters of the latent state process and the functions corresponding to the J states. We also obtain standard errors for the parameter estimates of the state process. We conduct simulation studies to analyse the frequentist properties of our estimates. We also apply the proposed methodology to the well-known motorcycle dataset treating the data as coming from more than one simulated accident run with unobserved run labels. Journal: Journal of Nonparametric Statistics Pages: 617-637 Issue: 4 Volume: 26 Year: 2014 Month: 12 X-DOI: 10.1080/10485252.2014.941364 File-URL: http://hdl.handle.net/10.1080/10485252.2014.941364 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:4:p:617-637 Template-Type: ReDIF-Article 1.0 Author-Name: Christophe Crambes Author-X-Name-First: Christophe Author-X-Name-Last: Crambes Author-Name: Ali Gannoun Author-X-Name-First: Ali Author-X-Name-Last: Gannoun Author-Name: Yousri Henchiri Author-X-Name-First: Yousri Author-X-Name-Last: Henchiri Title: Modelling functional additive quantile regression using support vector machines approach Abstract: This work deals with conditional quantiles estimation when several functional covariates are involved, via a support vector machines nonparametric methodology. We establish weak consistency of this estimator. To fit the additive components, we use an ordinary backfitting procedure combined with an iterative reweighted least-squares procedure to solve the penalised minimisation problem. This procedure makes it possible to derive a split sample method for choosing the hyper-parameters of the model. The performances of the proposed technique, in terms of forecast accuracy, are evaluated through simulation and a real dataset study. Journal: Journal of Nonparametric Statistics Pages: 639-668 Issue: 4 Volume: 26 Year: 2014 Month: 12 X-DOI: 10.1080/10485252.2014.941365 File-URL: http://hdl.handle.net/10.1080/10485252.2014.941365 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:4:p:639-668 Template-Type: ReDIF-Article 1.0 Author-Name: Sigve Hovda Author-X-Name-First: Sigve Author-X-Name-Last: Hovda Title: Using pseudometrics in kernel density estimation Abstract: Common kernel density estimators (KDE) are generalised, which involve that assumptions on the kernel of the distribution can be given. Instead of using metrics as input to the kernels, the new estimators use parameterisable pseudometrics. In general, the volumes of the balls in pseudometric spaces are dependent on both the radius and the location of the centre. To enable constant smoothing, the volumes of the balls need to be calculated and analytical expressions are preferred for computational reasons. Two suitable parametric families of pseudometrics are identified. One of them has common KDE as special cases. In a few experiments, the proposed estimators show increased statistical power when proper assumptions are made. As a consequence, this paper describes an approach, where partial knowledge about the distribution can be used effectively. Furthermore, it is suggested that the new estimators are adequate for statistical learning algorithms such as regression and classification. Journal: Journal of Nonparametric Statistics Pages: 669-696 Issue: 4 Volume: 26 Year: 2014 Month: 12 X-DOI: 10.1080/10485252.2014.944524 File-URL: http://hdl.handle.net/10.1080/10485252.2014.944524 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:4:p:669-696 Template-Type: ReDIF-Article 1.0 Author-Name: Taoufik Bouezmarni Author-X-Name-First: Taoufik Author-X-Name-Last: Bouezmarni Author-Name: Abderrahim Taamouti Author-X-Name-First: Abderrahim Author-X-Name-Last: Taamouti Title: Nonparametric tests for conditional independence using conditional distributions Abstract: The concept of causality is naturally defined in terms of conditional distribution, however almost all the empirical works focus on causality in mean. This paper aims to propose a nonparametric statistic to test the conditional independence and Granger non-causality between two variables conditionally on another one. The test statistic is based on the comparison of conditional distribution functions using an L₂ metric. We use Nadaraya-Watson method to estimate the conditional distribution functions. We establish the asymptotic size and power properties of the test statistic and we motivate the validity of the local bootstrap. We ran a simulation experiment to investigate the finite sample properties of the test and we illustrate its practical relevance by examining the Granger non-causality between S&P 500 Index returns and VIX volatility index. Contrary to the conventional t-test which is based on a linear mean-regression, we find that VIX index predicts excess returns both at short and long horizons. Journal: Journal of Nonparametric Statistics Pages: 697-719 Issue: 4 Volume: 26 Year: 2014 Month: 12 X-DOI: 10.1080/10485252.2014.945447 File-URL: http://hdl.handle.net/10.1080/10485252.2014.945447 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:4:p:697-719 Template-Type: ReDIF-Article 1.0 Author-Name: Asuman Turkmen Author-X-Name-First: Asuman Author-X-Name-Last: Turkmen Author-Name: Omer Ozturk Author-X-Name-First: Omer Author-X-Name-Last: Ozturk Title: Rank-based ridge estimation in multiple linear regression Abstract: Multicollinearity and model misspecification are frequently encountered problems in practice that produce undesirable effects on classical ordinary least squares (OLS) regression estimator. The ridge regression estimator is an important tool to reduce the effects of multicollinearity, but it is still sensitive to a model misspecification of error distribution. Although rank-based statistical inference has desirable robustness properties compared to the OLS procedures, it can be unstable in the presence of multicollinearity. This paper introduces a rank regression estimator for regression parameters and develops tests for general linear hypotheses in a multiple linear regression model. The proposed estimator and the tests have desirable robustness features against the multicollinearity and model misspecification of error distribution. Asymptotic behaviours of the proposed estimator and the test statistics are investigated. Real and simulated data sets are used to demonstrate the feasibility and the performance of the estimator and the tests. Journal: Journal of Nonparametric Statistics Pages: 737-754 Issue: 4 Volume: 26 Year: 2014 Month: 12 X-DOI: 10.1080/10485252.2014.964714 File-URL: http://hdl.handle.net/10.1080/10485252.2014.964714 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:4:p:737-754 Template-Type: ReDIF-Article 1.0 Author-Name: Wai-Yin Poon Author-X-Name-First: Wai-Yin Author-X-Name-Last: Poon Author-Name: Hai-Bin Wang Author-X-Name-First: Hai-Bin Author-X-Name-Last: Wang Title: Multivariate partially linear single-index models: Bayesian analysis Abstract: Partially linear single-index models play important roles in advanced non-/semi-parametric statistics due to their generality and flexibility. We generalise these models from univariate response to multivariate responses. A Bayesian method with free-knot spline is used to analyse the proposed models, including the estimation and the prediction, and a Metropolis-within-Gibbs sampler is provided for posterior exploration. We also utilise the partially collapsed idea in our algorithm to speed up the convergence. The proposed models and methods of analysis are demonstrated by simulation studies and are applied to a real data set. Journal: Journal of Nonparametric Statistics Pages: 755-768 Issue: 4 Volume: 26 Year: 2014 Month: 12 X-DOI: 10.1080/10485252.2014.965706 File-URL: http://hdl.handle.net/10.1080/10485252.2014.965706 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:4:p:755-768 Template-Type: ReDIF-Article 1.0 Author-Name: R. Hilton Author-X-Name-First: R. Author-X-Name-Last: Hilton Author-Name: N. Serban Author-X-Name-First: N. Author-X-Name-Last: Serban Title: Theoretical limits of component identification in a separable nonlinear least-squares problem Abstract: We provide theoretical insights into component identification in a separable nonlinear least-squares problem in which the model is a linear combination of nonlinear functions (called components in this paper). Within this research, we assume that the number of components is unknown. The objective of this paper is to understand the limits of component discovery under the assumed model. We focus on two aspects. One is sensitivity analysis referring to the ability of separating regression components from noise. The second is resolution analysis referring to the ability of de-mixing components that have similar location parameters. We use a wavelet transformation that allows to zoom in at different levels of details in the observed data. We further apply these theoretical insights to provide a road map on how to detect components in more realistic settings such as a two-dimensional nuclear magnetic resonance experiment for protein structure determination. Journal: Journal of Nonparametric Statistics Pages: 769-791 Issue: 4 Volume: 26 Year: 2014 Month: 12 X-DOI: 10.1080/10485252.2014.965707 File-URL: http://hdl.handle.net/10.1080/10485252.2014.965707 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:26:y:2014:i:4:p:769-791 Template-Type: ReDIF-Article 1.0 Author-Name: Tina Felber Author-X-Name-First: Tina Author-X-Name-Last: Felber Author-Name: Michael Kohler Author-X-Name-First: Michael Author-X-Name-Last: Kohler Author-Name: Adam Krzyżak Author-X-Name-First: Adam Author-X-Name-Last: Krzyżak Title: Adaptive density estimation based on real and artificial data Abstract: Let X, X₁, X₂, ... be independent and identically distributed ℝ-super-d-valued random variables and let m:ℝ-super-d→ℝ be a measurable function such that a density f of Y=m(X) exists. The problem of estimating f based on a sample of the distribution of (X,Y) and on additional independent observations of X is considered. Two kernel density estimates are compared: the standard kernel density estimate based on the y-values of the sample of (X,Y), and a kernel density estimate based on artificially generated y-values corresponding to the additional observations of X. It is shown that under suitable smoothness assumptions on f and m the rate of convergence of the L₁ error of the latter estimate is better than that of the standard kernel density estimate. Furthermore, a density estimate defined as convex combination of these two estimates is considered and a data-driven choice of its parameters (bandwidths and weight of the convex combination) is proposed and analysed. Journal: Journal of Nonparametric Statistics Pages: 1-18 Issue: 1 Volume: 27 Year: 2015 Month: 3 X-DOI: 10.1080/10485252.2014.969729 File-URL: http://hdl.handle.net/10.1080/10485252.2014.969729 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:1:p:1-18 Template-Type: ReDIF-Article 1.0 Author-Name: Minggen Lu Author-X-Name-First: Minggen Author-X-Name-Last: Lu Title: Spline estimation of generalised monotonic regression Abstract: We develop a simple and practical, yet flexible spline estimation method for semiparametric generalised linear models with monotonicity constraints. We propose to approximate the unknown monotone function by monotone B-splines, and employ generalised Rosen algorithm to compute the estimates. We show that the spline estimate of the nonparametric component achieves the optimal rate of convergence under the smooth condition, and that the estimates of regression parameters are asymptotically normal and efficient. The spline-based semiparametric likelihood ratio test (LRT) is also established. Moreover, a direct variance estimation method based on least-squares estimation is proposed. The finite sample performance of the spline estimates is evaluated by a Monte Carlo study. The methodology is illustrated on an air pollution study. Journal: Journal of Nonparametric Statistics Pages: 19-39 Issue: 1 Volume: 27 Year: 2015 Month: 3 X-DOI: 10.1080/10485252.2014.972953 File-URL: http://hdl.handle.net/10.1080/10485252.2014.972953 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:1:p:19-39 Template-Type: ReDIF-Article 1.0 Author-Name: Masayuki Hirukawa Author-X-Name-First: Masayuki Author-X-Name-Last: Hirukawa Author-Name: Mari Sakudo Author-X-Name-First: Mari Author-X-Name-Last: Sakudo Title: Family of the generalised gamma kernels: a generator of asymmetric kernels for nonnegative data Abstract: Unlike symmetric kernels, so far exploring asymptotics on asymmetric kernels has relied on diversified approaches. This paper proposes a family of the generalised gamma (GG) kernels that is built on the probability density function of the GG distribution [Stacy, E.W. (1962), 'A Generalization of the Gamma Distribution', Annals of Mathematical Statistics, 33, 1187-1192] and a few common conditions. The family can generate asymmetric kernels that share appealing properties with the modified gamma kernel [Chen, S.X. (2000), 'Probability Density Function Estimation Using Gamma Kernels', Annals of the Institute of Statistical Mathematics, 52, 471-480]. Asymptotics on the kernels generated from the family can be delivered by manipulating the conditions directly, as with symmetric kernels. Journal: Journal of Nonparametric Statistics Pages: 41-63 Issue: 1 Volume: 27 Year: 2015 Month: 3 X-DOI: 10.1080/10485252.2014.998669 File-URL: http://hdl.handle.net/10.1080/10485252.2014.998669 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:1:p:41-63 Template-Type: ReDIF-Article 1.0 Author-Name: Mohamed Chaouch Author-X-Name-First: Mohamed Author-X-Name-Last: Chaouch Author-Name: Salah Khardani Author-X-Name-First: Salah Author-X-Name-Last: Khardani Title: Randomly censored quantile regression estimation using functional stationary ergodic data Abstract: This paper investigates the conditional quantile estimation of a randomly censored scalar response variable given a functional random covariate (i.e. valued in some infinite-dimensional space) whenever a stationary ergodic data are considered. A kernel-type estimator of the conditional quantile function is introduced. Then, a strong consistency rate as well as the asymptotic distribution of the estimator are established under mild assumptions. A simulation study is considered to show the performance of the proposed estimator. An application to the electricity peak demand prediction using censored smart meter data is also provided. Journal: Journal of Nonparametric Statistics Pages: 65-87 Issue: 1 Volume: 27 Year: 2015 Month: 3 X-DOI: 10.1080/10485252.2014.982651 File-URL: http://hdl.handle.net/10.1080/10485252.2014.982651 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:1:p:65-87 Template-Type: ReDIF-Article 1.0 Author-Name: Weixuan Zhu Author-X-Name-First: Weixuan Author-X-Name-Last: Zhu Author-Name: Fabrizio Leisen Author-X-Name-First: Fabrizio Author-X-Name-Last: Leisen Title: A multivariate extension of a vector of two-parameter Poisson-Dirichlet processes Abstract: In the big data era there is a growing need to model the main features of large and non-trivial data sets. This paper proposes a Bayesian nonparametric prior for modelling situations where data are divided into different units with different densities, allowing information pooling across the groups. Leisen and Lijoi [(2011), 'Vectors of Poisson-Dirichlet processes', J. Multivariate Anal., 102, 482-495] introduced a bivariate vector of random probability measures with Poisson-Dirichlet marginals where the dependence is induced through a Lévy's Copula. In this paper the same approach is used for generalising such a vector to the multivariate setting. A first important contribution is the derivation of the Laplace functional transform which is non-trivial in the multivariate setting. The Laplace transform is the basis to derive the exchangeable partition probability function (EPPF) and, as a second contribution, we provide an expression of the EPPF for the multivariate setting. Finally, a novel Markov Chain Monte Carlo algorithm for evaluating the EPPF is introduced and tested. In particular, numerical illustrations of the clustering behaviour of the new prior are provided. Journal: Journal of Nonparametric Statistics Pages: 89-105 Issue: 1 Volume: 27 Year: 2015 Month: 3 X-DOI: 10.1080/10485252.2014.966103 File-URL: http://hdl.handle.net/10.1080/10485252.2014.966103 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:1:p:89-105 Template-Type: ReDIF-Article 1.0 Author-Name: Stéphan Clémençon Author-X-Name-First: Stéphan Author-X-Name-Last: Clémençon Author-Name: Sylvain Robbiano Author-X-Name-First: Sylvain Author-X-Name-Last: Robbiano Title: The TreeRank Tournament algorithm for multipartite ranking Abstract: Whereas various efficient learning algorithms have been recently proposed to perform bipartite ranking tasks, cast as receiver operating characteristic (ROC) curve optimisation, no method fully tailored to K-partite ranking when K≥3 has been documented in the statistical learning literature yet. The goal is to optimise the ROC manifold, or summary criteria such as its volume, the gold standard for assessing performance in K-partite ranking. It is the main purpose of this paper to describe at length an efficient approach to recursive maximisation of the ROC surface, extending the TreeRank methodology originally tailored for the bipartite situation (i.e. when K=2). The main barrier arises from the fact that, in contrast to the bipartite case, the volume under the ROC surface criterion of any scoring rule taking K≥3 values cannot be interpreted as a cost-sensitive misclassification error and no method is readily available to perform the recursive optimisation stage. The learning algorithm we propose, called TreeRank Tournament (referred to as 'TRT' in the tables), breaks it and builds recursively an ordered partition of the feature space. It defines a piecewise scoring function whose ROC manifold can be remarkably interpreted as a statistical version of an adaptive piecewise linear approximant of the optimal ROC manifold. Rate bounds in sup norm describing the generalisation ability of the scoring rule thus built are established and numerical results illustrating the performance of the TRT approach, compared to that of natural competitors such as aggregation methods, are also displayed. Journal: Journal of Nonparametric Statistics Pages: 107-126 Issue: 1 Volume: 27 Year: 2015 Month: 3 X-DOI: 10.1080/10485252.2014.967770 File-URL: http://hdl.handle.net/10.1080/10485252.2014.967770 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:1:p:107-126 Template-Type: ReDIF-Article 1.0 Author-Name: Uttam Bandyopadhyay Author-X-Name-First: Uttam Author-X-Name-Last: Bandyopadhyay Author-Name: Suryasish Chatterjee Author-X-Name-First: Suryasish Author-X-Name-Last: Chatterjee Title: Nonparametric analysis of the two-period two-treatment crossover design Abstract: The paper describes a nonparametric model for the analysis of the two-treatment, two-period, four-sequence crossover design. Tests for the equality of treatment effects and for the absence of carryover effects are provided. Some relevant asymptotic results of the proposed tests are obtained and compared with the existing nonparametric and parametric competitors via simulation. It is shown that the proposed tests are comparable to or better than the competitors in terms of type I error and power. Journal: Journal of Nonparametric Statistics Pages: 127-148 Issue: 1 Volume: 27 Year: 2015 Month: 3 X-DOI: 10.1080/10485252.2014.970552 File-URL: http://hdl.handle.net/10.1080/10485252.2014.970552 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:1:p:127-148 Template-Type: ReDIF-Article 1.0 Author-Name: I. Votsi Author-X-Name-First: I. Author-X-Name-Last: Votsi Author-Name: N. Limnios Author-X-Name-First: N. Author-X-Name-Last: Limnios Title: Estimation of the intensity of the hitting time for semi-Markov chains and hidden Markov renewal chains Abstract: In this paper, we focus on a fundamental reliability measure, the discrete-time intensity of the hitting time (DTIHT), which is the discrete analogue of the rate of occurrence of failures. The problem of evaluating and estimating the DTIHT is addressed for the first time for semi-Markov chains. First, a simple formula for the evaluation of the DTIHT is derived. Following the previous result, a statistical estimator of this plug-in type function is proposed. The main results given here are the asymptotic properties of this estimator, including the strong consistency and the asymptotic normality. Second, the DTIHT is investigated for hidden Markov renewal chains. Following its evaluation, a statistical estimator is suggested whose asymptotic properties are studied. Finally, we give some numerical examples for illustration purposes. The derived models and results can be used to typical reliability problems encountered in different scientific disciplines. Journal: Journal of Nonparametric Statistics Pages: 149-166 Issue: 2 Volume: 27 Year: 2015 Month: 6 X-DOI: 10.1080/10485252.2015.1009369 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1009369 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:2:p:149-166 Template-Type: ReDIF-Article 1.0 Author-Name: Yoonsuh Jung Author-X-Name-First: Yoonsuh Author-X-Name-Last: Jung Author-Name: Jianhua Hu Author-X-Name-First: Jianhua Author-X-Name-Last: Hu Title: A K-fold averaging cross-validation procedure Abstract: Cross-validation (CV) type of methods have been widely used to facilitate model estimation and variable selection. In this work, we suggest a new K-fold CV procedure to select a candidate 'optimal' model from each hold-out fold and average the K candidate 'optimal' models to obtain the ultimate model. Due to the averaging effect, the variance of the proposed estimates can be significantly reduced. This new procedure results in more stable and efficient parameter estimation than the classical K-fold CV procedure. In addition, we show the asymptotic equivalence between the proposed and classical CV procedures in the linear regression setting. We also demonstrate the broad applicability of the proposed procedure via two examples of parameter sparsity regularisation and quantile smoothing splines modelling. We illustrate the promise of the proposed method through simulations and a real data example. Journal: Journal of Nonparametric Statistics Pages: 167-179 Issue: 2 Volume: 27 Year: 2015 Month: 6 X-DOI: 10.1080/10485252.2015.1010532 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1010532 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:2:p:167-179 Template-Type: ReDIF-Article 1.0 Author-Name: Qingzhu Lei Author-X-Name-First: Qingzhu Author-X-Name-Last: Lei Author-Name: Yongsong Qin Author-X-Name-First: Yongsong Author-X-Name-Last: Qin Title: Confidence intervals for probability density functions under strong mixing samples Abstract: It is shown that the empirical likelihood (EL) ratio statistic for a probability density function (p.d.f.) is asymptotically

-type distributed under a strong mixing sample, which is used to obtain an EL-based confidence interval (CI) for the p.d.f. Results of a simulation study on the finite sample performance of the CI are reported. Journal: Journal of Nonparametric Statistics Pages: 181-193 Issue: 2 Volume: 27 Year: 2015 Month: 6 X-DOI: 10.1080/10485252.2015.1037303 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1037303 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:2:p:181-193 Template-Type: ReDIF-Article 1.0 Author-Name: Clemontina A. Davenport Author-X-Name-First: Clemontina A. Author-X-Name-Last: Davenport Author-Name: Arnab Maity Author-X-Name-First: Arnab Author-X-Name-Last: Maity Author-Name: Yichao Wu Author-X-Name-First: Yichao Author-X-Name-Last: Wu Title: Parametrically guided estimation in nonparametric varying coefficient models with quasi-likelihood Abstract: Varying coefficient models (VCMs) allow us to generalise standard linear regression models to incorporate complex covariate effects by modelling the regression coefficients as functions of another covariate. For nonparametric varying coefficients, we can borrow the idea of parametrically guided estimation to improve asymptotic bias. In this paper, we develop a guided estimation procedure for the nonparametric VCMs. Asymptotic properties are established for the guided estimators and a method of bandwidth selection via bias-variance tradeoff is proposed. We compare the performance of the guided estimator with that of the unguided estimator via both simulation and real data examples. Journal: Journal of Nonparametric Statistics Pages: 195-213 Issue: 2 Volume: 27 Year: 2015 Month: 6 X-DOI: 10.1080/10485252.2015.1026903 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1026903 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:2:p:195-213 Template-Type: ReDIF-Article 1.0 Author-Name: Brice M. Nguelifack Author-X-Name-First: Brice M. Author-X-Name-Last: Nguelifack Author-Name: Eddy A. Kwessi Author-X-Name-First: Eddy A. Author-X-Name-Last: Kwessi Author-Name: Asheber Abebe Author-X-Name-First: Asheber Author-X-Name-Last: Abebe Title: Generalised signed-rank estimation for nonlinear models with multidimensional indices Abstract: We consider a nonlinear regression model when the index variable is multidimensional. Such models are useful in signal processing, texture modelling, and spatio-temporal data analysis. A generalised form of the signed-rank estimator of the nonlinear regression coefficients is proposed. This general form of the signed-rank (SR) estimator includes

estimators and hybrid variants. Sufficient conditions for strong consistency and asymptotic normality of the estimator are given. It is shown that the rate of convergence to normality can be different from

. The sufficient conditions are weak in the sense that they are satisfied by harmonic-type functions for which results in the current literature may not apply. A simulation study shows that certain generalised SR estimators (e.g. signed rank) perform better in recovering signals than others (e.g. least squares) when the error distribution is contaminated or is heavy-tailed. Journal: Journal of Nonparametric Statistics Pages: 215-228 Issue: 2 Volume: 27 Year: 2015 Month: 6 X-DOI: 10.1080/10485252.2015.1029474 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1029474 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:2:p:215-228 Template-Type: ReDIF-Article 1.0 Author-Name: Sucharita Ghosh Author-X-Name-First: Sucharita Author-X-Name-Last: Ghosh Title: Surface estimation under local stationarity Abstract: Consider a nonparametric regression model involving spatial observations that are nonlinear transformations of a latent Gaussian random field. We address estimation of the variance of the Priestley-Chao kernel estimator of the surface by using a local stationarity-type property which is a result of the assumed transformation. It turns out that it is possible to avoid estimation of the various nuisance parameters so as to estimate the leading term of the asymptotic variance of the estimator. We also address uniform convergence of the nonparametric surface estimator, under short-memory and long-memory correlations in the data. Journal: Journal of Nonparametric Statistics Pages: 229-240 Issue: 2 Volume: 27 Year: 2015 Month: 6 X-DOI: 10.1080/10485252.2015.1029473 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1029473 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:2:p:229-240 Template-Type: ReDIF-Article 1.0 Author-Name: Heng Lian Author-X-Name-First: Heng Author-X-Name-Last: Lian Author-Name: Zengyan Fan Author-X-Name-First: Zengyan Author-X-Name-Last: Fan Title: Estimation of a sparse and spiked covariance matrix Abstract: We suggest a method for estimating a covariance matrix that can be represented as a sum of a sparse low-rank matrix and a diagonal matrix. Our formulation is based on penalized quadratic loss, which is a convex problem that can be solved via incremental gradient and proximal method. In contrast to other spiked covariance matrix estimation approaches that are related to principal component analysis and factor analysis, our method has a simple formulation and does not constrain entire rows and columns of the matrix to be zero. We further discuss a penalized entropy loss method that is nevertheless nonconvex and necessitates a majorization-minimization algorithm in combination with the incremental gradient and proximal method. We carry out simulations to demonstrate the finite-sample properties focusing on high-dimensional covariance matrices. Finally, the proposed method is illustrated using a gene expression data set. Journal: Journal of Nonparametric Statistics Pages: 241-252 Issue: 2 Volume: 27 Year: 2015 Month: 6 X-DOI: 10.1080/10485252.2015.1022545 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1022545 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:2:p:241-252 Template-Type: ReDIF-Article 1.0 Author-Name: Yuan Xue Author-X-Name-First: Yuan Author-X-Name-Last: Xue Author-Name: Xiangrong Yin Author-X-Name-First: Xiangrong Author-X-Name-Last: Yin Title: Sufficient dimension folding for a functional of conditional distribution of matrix- or array-valued objects Abstract: In this paper, we introduce sufficient dimension folding for a functional of conditional distribution of matrix- or array-valued objects, which suggests a new concept of central T dimension folding subspace (CTDFS). CTDFS includes central dimension folding subspace and central mean dimension folding subspace as special cases. A class of estimation methods on CTDFS is introduced. In particular, we focus on sufficient dimension folding for robust functionals. In this paper, we pay special attention to the central quantile dimension folding subspace (CQDFS), a widely interesting case of CTDFS, and develop new estimation methods. The performances of the proposed estimation methods on estimating the CQDFS are demonstrated by simulations and by analysing the primary biliary cirrhosis data. Journal: Journal of Nonparametric Statistics Pages: 253-269 Issue: 2 Volume: 27 Year: 2015 Month: 6 X-DOI: 10.1080/10485252.2015.1022176 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1022176 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:2:p:253-269 Template-Type: ReDIF-Article 1.0 Author-Name: Ann-Kathrin Bott Author-X-Name-First: Ann-Kathrin Author-X-Name-Last: Bott Author-Name: Tina Felber Author-X-Name-First: Tina Author-X-Name-Last: Felber Author-Name: Michael Kohler Author-X-Name-First: Michael Author-X-Name-Last: Kohler Title: Estimation of a density in a simulation model Abstract: The problem of estimating density in a simulation model is considered. Given a value of an

-valued random input parameter X, the value of a real-valued random variable

is computed. Here

is a function which measures the quality

of a technical system with input X. It is assumed that X and Y have densities. Given a sample of

, the task is to estimate the density of Y. In a first step we estimate m and the density of X. Using these estimators we compute in a second step an estimator of the density of Y. Results concerning the

-consistency and the rate of convergence are proven and the finite sample behaviour of the estimators is illustrated by applying them to simulated and real data. Journal: Journal of Nonparametric Statistics Pages: 271-285 Issue: 3 Volume: 27 Year: 2015 Month: 9 X-DOI: 10.1080/10485252.2015.1049601 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1049601 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:3:p:271-285 Template-Type: ReDIF-Article 1.0 Author-Name: C. Chesneau Author-X-Name-First: C. Author-X-Name-Last: Chesneau Author-Name: F. Comte Author-X-Name-First: F. Author-X-Name-Last: Comte Author-Name: G. Mabon Author-X-Name-First: G. Author-X-Name-Last: Mabon Author-Name: F. Navarro Author-X-Name-First: F. Author-X-Name-Last: Navarro Title: Estimation of convolution in the model with noise Abstract: We investigate the estimation of the ℓ-fold convolution of the density of an unobserved variable X from n i.i.d. observations of the convolution model

. We first assume that the density of the noise ϵ is known and define non-adaptive estimators, for which we provide bounds for the mean integrated squared error. In particular, under some smoothness assumptions on the densities of X and ϵ, we prove that the parametric rate of convergence

can be attained. Then, we construct an adaptive estimator using a penalisation approach having similar performances to the non-adaptive one. The price for its adaptivity is a logarithmic term. The results are extended to the case of unknown noise density, under the condition that an independent noise sample is available. Lastly, we report a simulation study to support our theoretical findings. Journal: Journal of Nonparametric Statistics Pages: 286-315 Issue: 3 Volume: 27 Year: 2015 Month: 9 X-DOI: 10.1080/10485252.2015.1041944 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1041944 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:3:p:286-315 Template-Type: ReDIF-Article 1.0 Author-Name: Germán Aneiros Author-X-Name-First: Germán Author-X-Name-Last: Aneiros Author-Name: Nengxiang Ling Author-X-Name-First: Nengxiang Author-X-Name-Last: Ling Author-Name: Philippe Vieu Author-X-Name-First: Philippe Author-X-Name-Last: Vieu Title: Error variance estimation in semi-functional partially linear regression models Abstract: This paper focuses on partially linear regression models with several real and functional covariates. The aim is to construct an estimate of the variance of the error. In our model, a real-valued response variable is explained by the sum of an unknown linear combination of the components of a multivariate random variable and an unknown transformation of a functional random variable, and the second sample moment based on residuals from a semiparametric fit is proposed for estimating the error variance. Then, the asymptotic normality and the law of the iterated logarithm of such estimator are obtained. Finally, a simulation study illustrates the finite sample behaviour of the estimator, while an application to real data shows the usefulness of the proposed methodology, more specifically for confidence region construction. Journal: Journal of Nonparametric Statistics Pages: 316-330 Issue: 3 Volume: 27 Year: 2015 Month: 9 X-DOI: 10.1080/10485252.2015.1042376 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1042376 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:3:p:316-330 Template-Type: ReDIF-Article 1.0 Author-Name: Jin Wang Author-X-Name-First: Jin Author-X-Name-Last: Wang Author-Name: Weihua Zhou Author-X-Name-First: Weihua Author-X-Name-Last: Zhou Title: Effect of kurtosis on efficiency of some multivariate medians Abstract: Up to now, various multivariate medians have been proposed. To support their applications, we study the effect of kurtosis on efficiency of some well-known multivariate medians. Results are established for the coordinatewise median, the spatial median, the Oja median, and their modified versions. Such results provide a basis for choosing among the multivariate medians in practical analyses. The effect of dimension on efficiency of those multivariate medians is also studied. It is found that the result of Brown [(1983), 'Statistical Uses of the Spatial Median', Journal of the Royal Statistical Society, Series B, 45, 25-30] for the spatial median and spherically symmetric normal distributions can be extended to some other medians and some non-normal distributions but does not hold in general. Journal: Journal of Nonparametric Statistics Pages: 331-348 Issue: 3 Volume: 27 Year: 2015 Month: 9 X-DOI: 10.1080/10485252.2015.1046450 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1046450 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:3:p:331-348 Template-Type: ReDIF-Article 1.0 Author-Name: Tao Hu Author-X-Name-First: Tao Author-X-Name-Last: Hu Author-Name: Yanping Qiu Author-X-Name-First: Yanping Author-X-Name-Last: Qiu Author-Name: Hengjian Cui Author-X-Name-First: Hengjian Author-X-Name-Last: Cui Title: Robust estimation of constant and time-varying parameters in nonlinear ordinary differential equation models Abstract: Ordinary differential equation (ODE) models are quite popular for modelling complex dynamic processes in many scientific fields, and the parameters in these models are usually unknown, and we need to estimate them using statistical methods. When some observations are contaminated, regular estimation methods, such as nonlinear least-square estimation, will bring large bias. In this paper, robust estimations of both constant and time-varying parameters in ODE models using M-estimators are proposed, and their asymptotic properties are obtained under some mild conditions. We focus on Huber M-estimator, and also provide a method to adjust the Huber parameter automatically to the observations. The proposed method is compared to existing methods in numerical simulations and CD8+ T cell data analysis. It is demonstrated that our method gain substantial efficiency as well as robust properties. Journal: Journal of Nonparametric Statistics Pages: 349-371 Issue: 3 Volume: 27 Year: 2015 Month: 9 X-DOI: 10.1080/10485252.2015.1042377 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1042377 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:3:p:349-371 Template-Type: ReDIF-Article 1.0 Author-Name: Thomas Verdebout Author-X-Name-First: Thomas Author-X-Name-Last: Verdebout Title: On some validity-robust tests for the homogeneity of concentrations on spheres Abstract: In this paper we tackle the problem of testing the homogeneity of concentrations for directional data. All the existing procedures for this problem are parametric procedures based on the assumption of a Fisher-von Mises-Langevin (FvML) distribution. We construct here a pseudo-FvML test and a rank-based Kruskal-Wallis-type test for this problem. The pseudo-FvML test improves on the traditional FvML parametric procedures by being asymptotically valid under the whole semiparametric class of rotationally symmetric distributions. Furthermore, it is asymptotically equivalent to the locally and asymptotically most stringent parametric FvML procedure in the FvML case. The Kruskal-Wallis rank-based test is also asymptotically valid under rotationally symmetric distributions and performs nicely under various important distributions. The finite-sample behaviour of the proposed tests is investigated by means of a Monte Carlo simulation. Journal: Journal of Nonparametric Statistics Pages: 372-383 Issue: 3 Volume: 27 Year: 2015 Month: 9 X-DOI: 10.1080/10485252.2015.1041945 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1041945 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:3:p:372-383 Template-Type: ReDIF-Article 1.0 Author-Name: Jun Li Author-X-Name-First: Jun Author-X-Name-Last: Li Title: Nonparametric multivariate statistical process control charts: a hypothesis testing-based approach Abstract: Nonparametric multivariate control charts are highly sought-after due to their flexibility to adapt to different distribution assumptions. However, most existing nonparametric multivariate control charts involve some tuning parameter, which needs to be pre-specified to implement those control charts. To choose the appropriate tuning parameter to achieve optimal performance, it usually requires the information about the out-of-control distribution. However, in practice, it is rarely known in advance what the out-of-control distribution is. In this paper, we propose a new nonparametric multivariate phase-II control chart using a hypothesis testing-based approach when a body of reference data (phase-I data) is available. The proposed control chart does not depend on any tuning parameter, and can be considered as a natural generalisation of the generalised likelihood ratio chart to the nonparametric setting. Our simulation study and real data analysis show that the proposed control chart performs well across a broad range of settings, and compares favourably with existing nonparametric multivariate control charts. Journal: Journal of Nonparametric Statistics Pages: 384-400 Issue: 3 Volume: 27 Year: 2015 Month: 9 X-DOI: 10.1080/10485252.2015.1062889 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1062889 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:3:p:384-400 Template-Type: ReDIF-Article 1.0 Author-Name: P. Cattiaux Author-X-Name-First: P. Author-X-Name-Last: Cattiaux Author-Name: José R. León Author-X-Name-First: José R. Author-X-Name-Last: León Author-Name: C. Prieur Author-X-Name-First: C. Author-X-Name-Last: Prieur Title: Recursive estimation for stochastic damping hamiltonian systems Abstract: In this paper, we complete our previous works on the nonparametric estimation of the characteristics (invariant density, drift term, variance term) of some ergodic hamiltonian systems, under partial observations. More precisely, we introduce recursive estimators using the full strength of the ergodic behaviour of the underlying process. We compare the theoretical properties of these estimators with the ones of the estimators we previously introduced in Cattiaux, Leon and Prieur ['Estimation for Stochastic Damping Hamiltonian Systems under Partial Observation. I. Invariant Density', Stochastic Processes and their Application, 124(3):1236-1260; 'Estimation for Stochastic Damping Hamiltonian Systems under Partial Observation. II. Drift term', ALEA Latin American Journal of Probability and Mathematical Statistics, 11, 359-384; 'Estimation for Stochastic Damping Hamiltonian Systems under Partial Observation. III. Diffusion term,' http://hal.archives-ouvertes.fr/hal-01044611. Journal: Journal of Nonparametric Statistics Pages: 401-424 Issue: 3 Volume: 27 Year: 2015 Month: 9 X-DOI: 10.1080/10485252.2015.1046451 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1046451 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:3:p:401-424 Template-Type: ReDIF-Article 1.0 Author-Name: Sébastien Loustau Author-X-Name-First: Sébastien Author-X-Name-Last: Loustau Author-Name: Clément Marteau Author-X-Name-First: Clément Author-X-Name-Last: Marteau Title: Noisy discriminant analysis with boundary assumptions Abstract: We address the problem of smooth discriminant analysis when data are collected from two samples with measurement errors. This problem turns to be an inverse problem and requires a specific treatment. In this context, we investigate consistency rates of convergence using both a margin assumption, and a complexity assumption in terms of entropy. In particular, we concentrate our attention on a boundary condition on the Bayes set and exhibits two distinct scenarii of convergence for the excess risk. For mildly ill-posed inverse problems, fast rates (i.e. faster than

) may occur whereas in the presence of one 'supersmooth' component for measurement errors, the excess risk is a negative power of

. Journal: Journal of Nonparametric Statistics Pages: 425-441 Issue: 4 Volume: 27 Year: 2015 Month: 12 X-DOI: 10.1080/10485252.2015.1067314 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1067314 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:4:p:425-441 Template-Type: ReDIF-Article 1.0 Author-Name: Włodzimierz Wysocki Author-X-Name-First: Włodzimierz Author-X-Name-Last: Wysocki Title: Kendall's tau and Spearman's rho for n-dimensional Archimedean copulas and their asymptotic properties Abstract: We derive formulas for the dependence measures

and

for Archimedean n-copulas. These measures are n-dimensional analogues of the popular nonparametric dependence measures: Kendall's tau and Spearman's rho. For

we obtain two formulas, both involving integrals of univariate functions. The formulas for

involve integrals of n-variate functions. We also obtain formulas for the three measures for copulas whose additive generators have completely monotone inverses. These formulas feature integrals of 2-variate functions (we use the Laplace transform). We study the asymptotic properties of the sequences

and

for a sequence

of Archimedean copulas with a common additive generator. We also investigate the limit of this sequence, which is an infinite-dimensional copula on the Hilbert cube. Journal: Journal of Nonparametric Statistics Pages: 442-459 Issue: 4 Volume: 27 Year: 2015 Month: 12 X-DOI: 10.1080/10485252.2015.1070849 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1070849 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:4:p:442-459 Template-Type: ReDIF-Article 1.0 Author-Name: Chiara Brombin Author-X-Name-First: Chiara Author-X-Name-Last: Brombin Author-Name: Luigi Salmaso Author-X-Name-First: Luigi Author-X-Name-Last: Salmaso Author-Name: Lara Fontanella Author-X-Name-First: Lara Author-X-Name-Last: Fontanella Author-Name: Luigi Ippoliti Author-X-Name-First: Luigi Author-X-Name-Last: Ippoliti Title: Nonparametric combination-based tests in dynamic shape analysis Abstract: Landmark-based geometric morphometric methods are probably the most widely used approaches for shape analysis. Much work has been done for static or cross-sectional shape analysis while considerably less research has focused on dynamic or longitudinal shapes. The question of analysing shape changes over time is a fundamental issue in many research fields. In this paper, as a motivating example, we consider the problem of describing the dynamics of facial expressions for which medical and sociological studies call for a proper differential analysis to distinguish their different characteristics. We address the problem from an inferential point of view testing whether landmark positions change over time, within each facial expression, and whether these changes are different between different expressions. As the shape changes over time completely depend on geometrical landmarks, part of the problem becomes finding the subset of landmarks which best describes the dynamics of the expressions. In this paper, we show by means of a motivating example related to the analysis of the FG-NET (Face and Gesture Recognition Research Network) database with facial expressions and emotions from the Technical University Munich [Wallhoff, F. (2006), 'Database with Facial Expressions and Emotions from Technical University of Munich (FEEDTUM)'], that NonParametric Combination (NPC) tests can be effective tools when testing whether there is a difference between dynamics of facial expressions or testing which of the landmarks are more informative in explaining their dynamics. In particular, we start analysing data by means of bivariate linear mixed-effects models and then we improve inferential results using the NPC methodology. Journal: Journal of Nonparametric Statistics Pages: 460-484 Issue: 4 Volume: 27 Year: 2015 Month: 12 X-DOI: 10.1080/10485252.2015.1071811 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1071811 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:4:p:460-484 Template-Type: ReDIF-Article 1.0 Author-Name: Lei Wang Author-X-Name-First: Lei Author-X-Name-Last: Wang Author-Name: Wendong Li Author-X-Name-First: Wendong Author-X-Name-Last: Li Author-Name: Guanfu Liu Author-X-Name-First: Guanfu Author-X-Name-Last: Liu Author-Name: Xiaolong Pu Author-X-Name-First: Xiaolong Author-X-Name-Last: Pu Title: Spatial median depth-based robust adjusted empirical likelihood Abstract: Empirical likelihood (EL) based inference for parameters defined by general estimating equations of Qin and Lawless [(1994), 'Empirical Likelihood and General Estimating Equations', The Annals of Statistics, 22, 300-325] remains an active research topic. However, the performance of the EL method can be hindered by non-robustness and empty set problems. In this paper, we propose a robust adjusted empirical likelihood (RAEL) to address these two problems simultaneously. The resulting RAEL ratio statistic is shown to have inherited the asymptotic properties of both the robust empirical likelihood and the adjusted empirical likelihood. The finite-sample performance of the proposed method is illustrated by simulation and two real-data examples are also presented. Journal: Journal of Nonparametric Statistics Pages: 485-502 Issue: 4 Volume: 27 Year: 2015 Month: 12 X-DOI: 10.1080/10485252.2015.1072179 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1072179 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:4:p:485-502 Template-Type: ReDIF-Article 1.0 Author-Name: Sudheesh K. Kattumannil Author-X-Name-First: Sudheesh K. Author-X-Name-Last: Kattumannil Author-Name: Deemat C. Mathew Author-X-Name-First: Deemat C. Author-X-Name-Last: Mathew Title: A Gini-based exact test for exponentiality against NBUE alternatives with censored observations Abstract: The Gini methodology in statistical inference and related area has got much attention in recent years. In this paper, using a characterisation based on the Gini index we develop a nonparametric test for testing exponentiality against new better than used in expectation class. We derive the exact null distribution of the proposed test statistic and then calculate the critical values for different sample sizes. Asymptotic properties of the test statistic are discussed. The test is compared with some other test by evaluating Pitman's asymptotic efficacy. We also discuss how to incorporate right-censored observations in our study. A simulation study is presented to demonstrate the performance of the testing method. Finally, we illustrated our test procedure using two real data sets. Journal: Journal of Nonparametric Statistics Pages: 503-515 Issue: 4 Volume: 27 Year: 2015 Month: 12 X-DOI: 10.1080/10485252.2015.1077242 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1077242 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:4:p:503-515 Template-Type: ReDIF-Article 1.0 Author-Name: Zonglin He Author-X-Name-First: Zonglin Author-X-Name-Last: He Author-Name: Jean D. Opsomer Author-X-Name-First: Jean D. Author-X-Name-Last: Opsomer Title: Local polynomial regression with an ordinal covariate Abstract: We are interested in fitting a nonparametric regression model to data when the covariate is an ordered categorical variable. We extend the local polynomial estimator, which normally requires continuous covariates, to a local polynomial estimator that allows for ordered categorical covariates. We derive the asymptotic conditional bias and variance under the assumption that the categories correspond to quantiles of an unobserved continuous latent variable. We conduct a simulation study with two patterns of ordinal data to evaluate our estimator. Journal: Journal of Nonparametric Statistics Pages: 516-531 Issue: 4 Volume: 27 Year: 2015 Month: 12 X-DOI: 10.1080/10485252.2015.1078462 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1078462 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:4:p:516-531 Template-Type: ReDIF-Article 1.0 Author-Name: Shuping Jiang Author-X-Name-First: Shuping Author-X-Name-Last: Jiang Author-Name: Lan Xue Author-X-Name-First: Lan Author-X-Name-Last: Xue Title: Globally consistent model selection in semi-parametric additive coefficient models Abstract: We study a penalised polynomial spline (PPS) method for model selection in additive coefficient models. It approximates nonparametric coefficient functions by polynomial splines and minimises the sum of squared errors subject to an additive penalty on the norms of spline functions. For non-convex penalty functions such as smoothly clipped absolute deviation (SCAD) penalty, we investigate the asymptotic properties of the global solution of the non-convex objective function. We establish explicitly that the oracle estimator is the global solution with probability approaching one. Therefore, the global solution enjoys both model estimation and selection consistency. In the literature, the asymptotic properties of local solutions rather than global solutions are well-established for non-convex penalty functions. Our theoretical results broaden the traditional understanding of the PPS method. Extensive Monte Carlo simulation studies show the proposed method performs well numerically. We also illustrate the use of the proposed method by analysing a housing price data set. Journal: Journal of Nonparametric Statistics Pages: 532-551 Issue: 4 Volume: 27 Year: 2015 Month: 12 X-DOI: 10.1080/10485252.2015.1083566 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1083566 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:27:y:2015:i:4:p:532-551 Template-Type: ReDIF-Article 1.0 Author-Name: Gaku Igarashi Author-X-Name-First: Gaku Author-X-Name-Last: Igarashi Title: Bias reductions for beta kernel estimation Abstract: The beta kernel estimator for a density with support

was discussed by Chen [(1999) ‘Beta Kernel Estimators for Density Functions’, Computational Statistics and Data Analysis, 31, 131--145]. In this paper, when the underlying density has a fourth-order derivative, we improve the beta kernel estimator using the bias correction techniques based on two beta kernel estimators with different smoothing parameters. As a result, we propose new bias corrected beta kernel estimators involving the digamma functions, and then establish their asymptotic properties. Simulation studies are conducted to illustrate the finite sample performance of the proposed estimators. Journal: Journal of Nonparametric Statistics Pages: 1-30 Issue: 1 Volume: 28 Year: 2016 Month: 3 X-DOI: 10.1080/10485252.2015.1112011 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1112011 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:1:p:1-30 Template-Type: ReDIF-Article 1.0 Author-Name: K. De Brabanter Author-X-Name-First: K. Author-X-Name-Last: De Brabanter Author-Name: Y. Liu Author-X-Name-First: Y. Author-X-Name-Last: Liu Author-Name: C. Hua Author-X-Name-First: C. Author-X-Name-Last: Hua Title: Convergence rates for uniform confidence intervals based on local polynomial regression estimators Abstract: We investigate the convergence rates of uniform bias-corrected confidence intervals for a smooth curve using local polynomial regression for both the interior and boundary region. We discuss the cases when the degree of the polynomial is odd and even. The uniform confidence intervals are based on the volume-of-tube formula modified for biased estimators. We empirically show that the proposed uniform confidence intervals attain, at least approximately, nominal coverage. Finally, we investigate the performance of the volume-of-tube based confidence intervals for independent non-Gaussian errors. Journal: Journal of Nonparametric Statistics Pages: 31-48 Issue: 1 Volume: 28 Year: 2016 Month: 3 X-DOI: 10.1080/10485252.2015.1113283 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1113283 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:1:p:31-48 Template-Type: ReDIF-Article 1.0 Author-Name: Mingqiu Wang Author-X-Name-First: Mingqiu Author-X-Name-Last: Wang Author-Name: Guo-Liang Tian Author-X-Name-First: Guo-Liang Author-X-Name-Last: Tian Title: Robust group non-convex estimations for high-dimensional partially linear models Abstract: High-dimensional data with a group structure of variables arise always in many contemporary statistical modelling problems. Heavy-tailed errors or outliers in the response often exist in these data. We consider robust group selection for partially linear models when the number of covariates can be larger than the sample size. The non-convex penalty function is applied to achieve both goals of variable selection and estimation in the linear part simultaneously, and we use polynomial splines to estimate the nonparametric component. Under regular conditions, we show that the robust estimator enjoys the oracle property. Simulation studies demonstrate the performance of the proposed method with samples of moderate size. The analysis of a real example illustrates that our method works well. Journal: Journal of Nonparametric Statistics Pages: 49-67 Issue: 1 Volume: 28 Year: 2016 Month: 3 X-DOI: 10.1080/10485252.2015.1112009 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1112009 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:1:p:49-67 Template-Type: ReDIF-Article 1.0 Author-Name: P.G. Sankaran Author-X-Name-First: P.G. Author-X-Name-Last: Sankaran Author-Name: S. Anjana Author-X-Name-First: S. Author-X-Name-Last: Anjana Title: Proportional cause-specific reversed hazards model Abstract: The proportional reversed hazards model explains the multiplicative effect of covariates on the baseline reversed hazard rate function of lifetimes. In the present study, we introduce a proportional cause-specific reversed hazards model. The proposed regression model facilitates the analysis of failure time data with multiple causes of failure under left censoring. We estimate the regression parameters using a partial likelihood approach. We provide Breslow's type estimators for the cumulative cause-specific reversed hazard rate functions. Asymptotic properties of the estimators are discussed. Simulation studies are conducted to assess their performance. We illustrate the applicability of the proposed model using a real data set. Journal: Journal of Nonparametric Statistics Pages: 68-83 Issue: 1 Volume: 28 Year: 2016 Month: 3 X-DOI: 10.1080/10485252.2015.1112010 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1112010 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:1:p:68-83 Template-Type: ReDIF-Article 1.0 Author-Name: Peter T. Kim Author-X-Name-First: Peter T. Author-X-Name-Last: Kim Author-Name: Ja-Yong Koo Author-X-Name-First: Ja-Yong Author-X-Name-Last: Koo Author-Name: Thanh Mai Pham Ngoc Author-X-Name-First: Thanh Author-X-Name-Last: Mai Pham Ngoc Title: Supersmooth testing on the sphere over analytic classes Abstract: We consider the nonparametric goodness-of-fit test of the uniform density on the sphere when we have observations whose density is the convolution of an error density and the true underlying density. We will deal specifically with the supersmooth error case which includes the Gaussian distribution. Similar to deconvolution density estimation, the smoother the error density the harder is the rate recovery of the test problem. When considering nonparametric alternatives expressed over analytic classes, we show that it is possible to obtain original separation rates much faster than any logarithmic power of the sample size according to the ratio of the regularity index of the analytic class and the smoothness degree of the error. Furthermore, we show that our fully data-driven statistical procedure attains these optimal rates. Journal: Journal of Nonparametric Statistics Pages: 84-115 Issue: 1 Volume: 28 Year: 2016 Month: 3 X-DOI: 10.1080/10485252.2015.1113284 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1113284 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:1:p:84-115 Template-Type: ReDIF-Article 1.0 Author-Name: Zhiyong Zhou Author-X-Name-First: Zhiyong Author-X-Name-Last: Zhou Author-Name: Zhengyan Lin Author-X-Name-First: Zhengyan Author-X-Name-Last: Lin Title: Asymptotic normality of locally modelled regression estimator for functional data Abstract: We focus on the nonparametric regression of a scalar response on a functional explanatory variable. As an alternative to the well-known Nadaraya-Watson estimator for regression function in this framework, the locally modelled regression estimator performs very well [cf. [Barrientos-Marin, J., Ferraty, F., and Vieu, P. (2010), ‘Locally Modelled Regression and Functional Data’, Journal of Nonparametric Statistics, 22, 617--632]. In this paper, the asymptotic properties of locally modelled regression estimator for functional data are considered. The mean-squared convergence as well as asymptotic normality for the estimator are established. We also adapt the empirical likelihood method to construct the point-wise confidence intervals for the regression function and derive the Wilk's phenomenon for the empirical likelihood inference. Furthermore, a simulation study is presented to illustrate our theoretical results. Journal: Journal of Nonparametric Statistics Pages: 116-131 Issue: 1 Volume: 28 Year: 2016 Month: 3 X-DOI: 10.1080/10485252.2015.1114112 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1114112 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:1:p:116-131 Template-Type: ReDIF-Article 1.0 Author-Name: Panagiotis Avramidis Author-X-Name-First: Panagiotis Author-X-Name-Last: Avramidis Title: Adaptive likelihood estimator of conditional variance function Abstract: Modelling volatility in the form of conditional variance function has been a popular method mainly due to its application in financial risk management. Among others, we distinguish the parametric GARCH models and the nonparametric local polynomial approximation using weighted least squares or gaussian likelihood function. We introduce an alternative likelihood estimate of conditional variance and we show that substitution of the error density with its estimate yields similar asymptotic properties, that is, the proposed estimate is adaptive to the error distribution. Theoretical comparison with existing estimates reveals substantial gains in efficiency, especially if error distribution has fatter tails than Gaussian distribution. Simulated data confirm the theoretical findings while an empirical example demonstrates the gains of the proposed estimate. Journal: Journal of Nonparametric Statistics Pages: 132-151 Issue: 1 Volume: 28 Year: 2016 Month: 3 X-DOI: 10.1080/10485252.2015.1122189 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1122189 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:1:p:132-151 Template-Type: ReDIF-Article 1.0 Author-Name: A. Dematteo Author-X-Name-First: A. Author-X-Name-Last: Dematteo Author-Name: S. Clémençon Author-X-Name-First: S. Author-X-Name-Last: Clémençon Title: On tail index estimation based on multivariate data Abstract: This article is devoted to the study of tail index estimation based on i.i.d. multivariate observations, drawn from a standard heavy-tailed distribution, that is, of which Pareto-like marginals share the same tail index. A multivariate central limit theorem for a random vector, whose components correspond to (possibly dependent) Hill estimators of the common tail index α, is established under mild conditions. We introduce the concept of (standard) heavy-tailed random vector of tail index α and show how this limit result can be used in order to build an estimator of α with small asymptotic mean squared error, through a proper convex linear combination of the coordinates. Beyond asymptotic results, simulation experiments illustrating the relevance of the approach promoted are also presented. Journal: Journal of Nonparametric Statistics Pages: 152-176 Issue: 1 Volume: 28 Year: 2016 Month: 3 X-DOI: 10.1080/10485252.2015.1124105 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1124105 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:1:p:152-176 Template-Type: ReDIF-Article 1.0 Author-Name: Seongil Jo Author-X-Name-First: Seongil Author-X-Name-Last: Jo Author-Name: Taeyoung Roh Author-X-Name-First: Taeyoung Author-X-Name-Last: Roh Author-Name: Taeryon Choi Author-X-Name-First: Taeryon Author-X-Name-Last: Choi Title: Bayesian spectral analysis models for quantile regression with Dirichlet process mixtures Abstract: This paper presents a Bayesian analysis of partially linear additive models for quantile regression. We develop a semiparametric Bayesian approach to quantile regression models using a spectral representation of the nonparametric regression functions and the Dirichlet process (DP) mixture for error distribution. We also consider Bayesian variable selection procedures for both parametric and nonparametric components in a partially linear additive model structure based on the Bayesian shrinkage priors via a stochastic search algorithm. Based on the proposed Bayesian semiparametric additive quantile regression model referred to as BSAQ, the Bayesian inference is considered for estimation and model selection. For the posterior computation, we design a simple and efficient Gibbs sampler based on a location-scale mixture of exponential and normal distributions for an asymmetric Laplace distribution, which facilitates the commonly used collapsed Gibbs sampling algorithms for the DP mixture models. Additionally, we discuss the asymptotic property of the sempiparametric quantile regression model in terms of consistency of posterior distribution. Simulation studies and real data application examples illustrate the proposed method and compare it with Bayesian quantile regression methods in the literature. Journal: Journal of Nonparametric Statistics Pages: 177-206 Issue: 1 Volume: 28 Year: 2016 Month: 3 X-DOI: 10.1080/10485252.2015.1124877 File-URL: http://hdl.handle.net/10.1080/10485252.2015.1124877 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:1:p:177-206 Template-Type: ReDIF-Article 1.0 Author-Name: Ryan Janicki Author-X-Name-First: Ryan Author-X-Name-Last: Janicki Author-Name: Tucker S. McElroy Author-X-Name-First: Tucker S. Author-X-Name-Last: McElroy Title: Hermite expansion and estimation of monotonic transformations of Gaussian data Abstract: This paper describes a semiparametric method for estimating a generic probability distribution using a basis expansion in

. We express the given distribution as a monotonic transformation of the Gaussian cumulative distribution function, expanded in a basis of Hermite polynomials. The coefficients in the basis expansion are functionals of the quantile function, and can be consistently estimated to give a smooth estimate of the transformation function. For situations in which the estimated function is not monotone, a projection approach is used to adjust the estimated transformation function to guarantee monotonicity. Two applications are presented which focus on the analysis of model residuals. The first is a data example which uses the residuals from the 2012 Small Area Income and Poverty Estimates model. The Hermite estimation method is applied to these residuals as a graphical method for detection of departures from normality and to construct credible intervals. The second example analyses residuals from time series models for the purpose of estimating the variance of the mean and median and comparing the results to the AR-sieve. This paper concludes with a set of numerical examples to illustrate the theoretical results. Journal: Journal of Nonparametric Statistics Pages: 207-234 Issue: 1 Volume: 28 Year: 2016 Month: 3 X-DOI: 10.1080/10485252.2016.1139880 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1139880 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:1:p:207-234 Template-Type: ReDIF-Article 1.0 Author-Name: Miguel Reyes Author-X-Name-First: Miguel Author-X-Name-Last: Reyes Author-Name: Mario Francisco-Fernández Author-X-Name-First: Mario Author-X-Name-Last: Francisco-Fernández Author-Name: Ricardo Cao Author-X-Name-First: Ricardo Author-X-Name-Last: Cao Title: Nonparametric kernel density estimation for general grouped data Abstract: Interval-grouped data are defined, in general, when the event of interest cannot be directly observed and it is only known to have been occurred within an interval. In this framework, a nonparametric kernel density estimator is proposed and studied. The approach is based on the classical Parzen--Rosenblatt estimator and on the generalisation of the binned kernel density estimator. The asymptotic bias and variance of the proposed estimator are derived under usual assumptions, and the effect of using non-equally spaced grouped data is analysed. Additionally, a plug-in bandwidth selector is proposed. Through a comprehensive simulation study, the behaviour of both the estimator and the plug-in bandwidth selector considering different scenarios of data grouping is shown. An application to real data confirms the simulation results, revealing the good performance of the estimator whenever data are not heavily grouped. Journal: Journal of Nonparametric Statistics Pages: 235-249 Issue: 2 Volume: 28 Year: 2016 Month: 6 X-DOI: 10.1080/10485252.2016.1163348 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1163348 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:2:p:235-249 Template-Type: ReDIF-Article 1.0 Author-Name: Zhong Guan Author-X-Name-First: Zhong Author-X-Name-Last: Guan Title: Efficient and robust density estimation using Bernstein type polynomials Abstract: A method of parameterising and smoothing the unknown underlying distributions using Bernstein type polynomials with positive coefficients is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed model which turns out to be a mixture of the beta distributions, beta

, for some optimal degree m. A simple change-point estimating method for choosing the optimal degree m of the approximate model is presented. The proposed method gives a maximum likelihood density estimate which is consistent in

distance at a nearly parametric rate

under some conditions. Simulation study shows that one can benefit from both the smoothness and the efficiency by using the proposed method which can also be used to estimate some population parameters such as the mean. The proposed methods are applied to three data sets of different types. Journal: Journal of Nonparametric Statistics Pages: 250-271 Issue: 2 Volume: 28 Year: 2016 Month: 6 X-DOI: 10.1080/10485252.2016.1163349 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1163349 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:2:p:250-271 Template-Type: ReDIF-Article 1.0 Author-Name: Masaki Narukawa Author-X-Name-First: Masaki Author-X-Name-Last: Narukawa Title: Semiparametric Whittle estimation of a cyclical long-memory time series based on generalised exponential models Abstract: This paper considers a semiparametric estimation of the memory parameter in a cyclical long-memory time series, which exhibits a strong dependence on cyclical behaviour, using the Whittle likelihood based on generalised exponential (GEXP) models. The proposed estimation is included in the so-called broadband or global method and uses information from the spectral density at all frequencies. We establish the consistency and the asymptotic normality of the estimated memory parameter for a linear process and thus do not require Gaussianity. A simulation study conducted using Monte Carlo experiments shows that the proposed estimation works well compared to other existing semiparametric estimations. Moreover, we provide an empirical application of the proposed estimation, applying it to the growth rate of Japan's industrial production index and detecting its cyclical persistence. Journal: Journal of Nonparametric Statistics Pages: 272-295 Issue: 2 Volume: 28 Year: 2016 Month: 6 X-DOI: 10.1080/10485252.2016.1163350 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1163350 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:2:p:272-295 Template-Type: ReDIF-Article 1.0 Author-Name: Michel Harel Author-X-Name-First: Michel Author-X-Name-Last: Harel Author-Name: Jean-François Lenain Author-X-Name-First: Jean-François Author-X-Name-Last: Lenain Author-Name: Joseph Ngatchou-Wandji Author-X-Name-First: Joseph Author-X-Name-Last: Ngatchou-Wandji Title: Asymptotic behaviour of binned kernel density estimators for locally non-stationary random fields Abstract: We investigate the asymptotic behaviour of binned kernel density estimators for dependent and locally non-stationary random fields converging to stationary random fields. We focus on the study of the bias and the asymptotic normality of the estimators. A simulation experiment conducted shows that both the kernel density estimator and the binned kernel density estimator have the same behavior and both estimate accurately the true density when the number of fields increases. We apply our results to the 2002 incidence rates of tuberculosis in the departments of France. Journal: Journal of Nonparametric Statistics Pages: 296-321 Issue: 2 Volume: 28 Year: 2016 Month: 6 X-DOI: 10.1080/10485252.2016.1163351 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1163351 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:2:p:296-321 Template-Type: ReDIF-Article 1.0 Author-Name: Eduardo L. Montoya Author-X-Name-First: Eduardo L. Author-X-Name-Last: Montoya Author-Name: Wendy Meiring Author-X-Name-First: Wendy Author-X-Name-Last: Meiring Title: An F-type test for detecting departure from monotonicity in a functional linear model Abstract: When studying associations between a functional covariate and scalar response using a functional linear model (FLM), scientific knowledge may indicate possible monotonicity of the unknown parameter curve. In this context, we propose an F-type test of monotonicity, based on a full versus reduced nested model structure, where the reduced model with monotonically constrained parameter curve is nested within an unconstrained FLM. For estimation under the unconstrained FLM, we consider two approaches: penalised least-squares and linear mixed model effects estimation. We use a smooth then monotonise approach to estimate the reduced model, within the null space of monotone parameter curves. A bootstrap procedure is used to simulate the null distribution of the test statistic. We present a simulation study of the power of the proposed test, and illustrate the test using data from a head and neck cancer study. Journal: Journal of Nonparametric Statistics Pages: 322-337 Issue: 2 Volume: 28 Year: 2016 Month: 6 X-DOI: 10.1080/10485252.2016.1163352 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1163352 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:2:p:322-337 Template-Type: ReDIF-Article 1.0 Author-Name: Jason Cleveland Author-X-Name-First: Jason Author-X-Name-Last: Cleveland Author-Name: Wei Wu Author-X-Name-First: Wei Author-X-Name-Last: Wu Author-Name: Anuj Srivastava Author-X-Name-First: Anuj Author-X-Name-Last: Srivastava Title: Norm-preserving constraint in the Fisher--Rao registration and its application in signal estimation Abstract: Registration of temporal observations is a fundamental problem in functional data analysis. Various frameworks have been developed over the past two decades where registrations are conducted based on optimal time warping between functions. Comparison of functions solely based on time warping, however, may have limited application, in particular when certain constraints are desired in the registration. In this paper, we study registration with norm-preserving constraint. A closely related problem is on signal estimation, where the goal is to estimate the ground-truth template given random observations with both compositional and additive noises. We propose to adopt the Fisher--Rao framework to compute the underlying template, and mathematically prove that such framework leads to a consistent estimator. We then illustrate the constrained Fisher--Rao registration using simulations as well as two real data sets. It is found that the constrained method is robust with respect to additive noise and has superior alignment and classification performance to conventional, unconstrained registration methods. Journal: Journal of Nonparametric Statistics Pages: 338-359 Issue: 2 Volume: 28 Year: 2016 Month: 6 X-DOI: 10.1080/10485252.2016.1163353 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1163353 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:2:p:338-359 Template-Type: ReDIF-Article 1.0 Author-Name: Min Chen Author-X-Name-First: Min Author-X-Name-Last: Chen Author-Name: Changbao Wu Author-X-Name-First: Changbao Author-X-Name-Last: Wu Author-Name: Mary E. Thompson Author-X-Name-First: Mary E. Author-X-Name-Last: Thompson Title: Mann--Whitney test with empirical likelihood methods for pretest--posttest studies Abstract: Pretest--posttest studies are an important and popular method for assessing the effectiveness of a treatment or an intervention in many scientific fields. While the treatment effect, measured as the difference between the two mean responses, is of primary interest, testing the difference of the two distribution functions for the treatment and the control groups is also an important problem. The Mann--Whitney test has been a standard tool for testing the difference of distribution functions with two independent samples. We develop empirical likelihood-based (EL) methods for the Mann--Whitney test to incorporate the two unique features of pretest--posttest studies: (i) the availability of baseline information for both groups; and (ii) the structure of the data with missing by design. Our proposed methods combine the standard Mann--Whitney test with the EL method of Huang, Qin and Follmann [(2008), ‘Empirical Likelihood-Based Estimation of the Treatment Effect in a Pretest--Posttest Study’, Journal of the American Statistical Association, 103(483), 1270--1280], the imputation-based empirical likelihood method of Chen, Wu and Thompson [(2015), ‘An Imputation-Based Empirical Likelihood Approach to Pretest--Posttest Studies’, The Canadian Journal of Statistics accepted for publication], and the jackknife empirical likelihood method of Jing, Yuan and Zhou [(2009), ‘Jackknife Empirical Likelihood’, Journal of the American Statistical Association, 104, 1224--1232]. Theoretical results are presented and finite sample performances of proposed methods are evaluated through simulation studies. Journal: Journal of Nonparametric Statistics Pages: 360-374 Issue: 2 Volume: 28 Year: 2016 Month: 6 X-DOI: 10.1080/10485252.2016.1163354 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1163354 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:2:p:360-374 Template-Type: ReDIF-Article 1.0 Author-Name: Liu Jicai Author-X-Name-First: Liu Author-X-Name-Last: Jicai Author-Name: Riquan Zhang Author-X-Name-First: Riquan Author-X-Name-Last: Zhang Author-Name: Weihua Zhao Author-X-Name-First: Weihua Author-X-Name-Last: Zhao Author-Name: Yazhao Lv Author-X-Name-First: Yazhao Author-X-Name-Last: Lv Title: Variable selection in partially linear hazard regression for multivariate failure time data Abstract: The aim of this paper is to explore variable selection approaches in the partially linear proportional hazards model for multivariate failure time data. A new penalised pseudo-partial likelihood method is proposed to select important covariates. Under certain regularity conditions, we establish the rate of convergence and asymptotic normality of the resulting estimates. We further show that the proposed procedure can correctly select the true submodel, as if it was known in advance. Both simulated and real data examples are presented to illustrate the proposed methodology. Journal: Journal of Nonparametric Statistics Pages: 375-394 Issue: 2 Volume: 28 Year: 2016 Month: 6 X-DOI: 10.1080/10485252.2016.1163355 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1163355 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:2:p:375-394 Template-Type: ReDIF-Article 1.0 Author-Name: Claudio G. Borroni Author-X-Name-First: Claudio G. Author-X-Name-Last: Borroni Author-Name: D. Michele Cifarelli Author-X-Name-First: D. Michele Author-X-Name-Last: Cifarelli Title: Some maximum-indifference estimators for the slope of a univariate linear model Abstract: As known, the least-squares estimator of the slope of a univariate linear model sets to zero the covariance between the regression residuals and the values of the explanatory variable. To prevent the estimation process from being influenced by outliers, which can be theoretically modelled by a heavy-tailed distribution for the error term, one can substitute covariance with some robust measures of association, for example Kendall's tau in the popular Theil--Sen estimator. In a scarcely known Italian paper, Cifarelli [(1978), ‘La Stima del Coefficiente di Regressione Mediante l'Indice di Cograduazione di Gini’, Rivista di matematica per le scienze economiche e sociali, 1, 7--38. A translation into English is available at http://arxiv.org/abs/1411.4809 and will appear in Decisions in Economics and Finance] shows that a gain of efficiency can be obtained by using Gini's cograduation index instead of Kendall's tau. This paper introduces a new estimator, derived from another association measure recently proposed. Such a measure is strongly related to Gini's cograduation index, as they are both built to vanish in the general framework of indifference. The newly proposed estimator is shown to be unbiased and asymptotically normally distributed. Moreover, all considered estimators are compared via their asymptotic relative efficiency and a small simulation study. Finally, some indications about the performance of the considered estimators in the presence of contaminated normal data are provided. Journal: Journal of Nonparametric Statistics Pages: 395-412 Issue: 2 Volume: 28 Year: 2016 Month: 6 X-DOI: 10.1080/10485252.2016.1163356 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1163356 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:2:p:395-412 Template-Type: ReDIF-Article 1.0 Author-Name: Bojana Milošević Author-X-Name-First: Bojana Author-X-Name-Last: Milošević Author-Name: Marko Obradović Author-X-Name-First: Marko Author-X-Name-Last: Obradović Title: Two-dimensional Kolmogorov-type goodness-of-fit tests based on characterisations and their asymptotic efficiencies Abstract: In this paper, new two-dimensional goodness-of-fit tests are proposed. They are of supremum type and are based on two different types of characterisations. The first type are those that involve functional equations that the distribution function satisfies, while the second type uses independence of some statistics. The asymptotics of the statistics is studied and Bahadur efficiencies of the tests against some close alternatives are calculated. In the process, a theorem on large deviations of Kolmogorov-type statistics has been extended to the multidimensional case. Journal: Journal of Nonparametric Statistics Pages: 413-427 Issue: 2 Volume: 28 Year: 2016 Month: 6 X-DOI: 10.1080/10485252.2016.1163358 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1163358 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:2:p:413-427 Template-Type: ReDIF-Article 1.0 Author-Name: Sophie Dabo-Niang Author-X-Name-First: Sophie Author-X-Name-Last: Dabo-Niang Author-Name: Camille Ternynck Author-X-Name-First: Camille Author-X-Name-Last: Ternynck Author-Name: Anne-Françoise Yao Author-X-Name-First: Anne-Françoise Author-X-Name-Last: Yao Title: Nonparametric prediction of spatial multivariate data Abstract: This paper investigates a nonparametric spatial predictor of a stationary multidimensional spatial process observed over a rectangular domain. The proposed predictor depends on two kernels in order to control both the distance between observations and that between spatial locations. The uniform almost complete consistency and the asymptotic normality of the kernel predictor are obtained when the sample considered is an alpha-mixing sequence. Numerical studies were carried out in order to illustrate the behaviour of our methodology both for simulated data and for an environmental data set. Journal: Journal of Nonparametric Statistics Pages: 428-458 Issue: 2 Volume: 28 Year: 2016 Month: 6 X-DOI: 10.1080/10485252.2016.1164313 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1164313 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:2:p:428-458 Template-Type: ReDIF-Article 1.0 Author-Name: Chuanhua Wei Author-X-Name-First: Chuanhua Author-X-Name-Last: Wei Author-Name: Xiaonan Wang Author-X-Name-First: Xiaonan Author-X-Name-Last: Wang Title: Liu-type estimator in semiparametric partially linear additive models Abstract: Partially linear additive model is useful in statistical modelling as a multivariate nonparametric fitting technique. This paper considers statistical inference for the semiparametric model in the presence of multicollinearity. Based on the profile least-squares (PL) approach and Liu estimation method, we propose a PL Liu estimator for the parametric component. When some additional linear restrictions on the parametric component are available, the corresponding restricted Liu estimator for the parametric component is constructed. The properties of the proposed estimators are derived. Some simulations are conducted to assess the performance of the proposed procedures and the results are satisfactory. Finally, a real data example is analysed. Journal: Journal of Nonparametric Statistics Pages: 459-468 Issue: 3 Volume: 28 Year: 2016 Month: 9 X-DOI: 10.1080/10485252.2016.1163357 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1163357 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:3:p:459-468 Template-Type: ReDIF-Article 1.0 Author-Name: M. Boukeloua Author-X-Name-First: M. Author-X-Name-Last: Boukeloua Author-Name: F. Messaci Author-X-Name-First: F. Author-X-Name-Last: Messaci Title: Asymptotic normality of kernel estimators based upon incomplete data Abstract: In this paper, we are concerned with nonparametric estimation of the density and the failure rate functions of a random variable X which is at risk of being censored. First, we establish the asymptotic normality of a kernel density estimator in a general censoring setup. Then, we apply our result in order to derive the asymptotic normality of both the density and the failure rate estimators in the cases of right, twice and doubly censored data. Finally, the performance and the asymptotic Gaussian behaviour of the studied estimators, based on either doubly or twice censored data, are illustrated through a simulation study. Journal: Journal of Nonparametric Statistics Pages: 469-486 Issue: 3 Volume: 28 Year: 2016 Month: 9 X-DOI: 10.1080/10485252.2016.1164312 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1164312 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:3:p:469-486 Template-Type: ReDIF-Article 1.0 Author-Name: Sophie Lambert-Lacroix Author-X-Name-First: Sophie Author-X-Name-Last: Lambert-Lacroix Author-Name: Laurent Zwald Author-X-Name-First: Laurent Author-X-Name-Last: Zwald Title: The adaptive BerHu penalty in robust regression Abstract: We intend to combine Huber's loss with an adaptive reversed version as a penalty function. The purpose is twofold: first we would like to propose an estimator that is robust to data subject to heavy-tailed errors or outliers. Second we hope to overcome the variable selection problem in the presence of highly correlated predictors. For instance, in this framework, the adaptive least absolute shrinkage and selection operator (lasso) is not a very satisfactory variable selection method, although it is a popular technique for simultaneous estimation and variable selection. We call this new penalty the adaptive BerHu penalty. As for elastic net penalty, small coefficients contribute through their

norm to this penalty while larger coefficients cause it to grow quadratically (as ridge regression). We will show that the estimator associated with Huber's loss combined with the adaptive BerHu penalty enjoys theoretical properties in the fixed design context. This approach is compared to existing regularisation methods such as adaptive elastic net and is illustrated via simulation studies and real data. Journal: Journal of Nonparametric Statistics Pages: 487-514 Issue: 3 Volume: 28 Year: 2016 Month: 9 X-DOI: 10.1080/10485252.2016.1190359 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1190359 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:3:p:487-514 Template-Type: ReDIF-Article 1.0 Author-Name: Lyu Ni Author-X-Name-First: Lyu Author-X-Name-Last: Ni Author-Name: Fang Fang Author-X-Name-First: Fang Author-X-Name-Last: Fang Title: Entropy-based model-free feature screening for ultrahigh-dimensional multiclass classification Abstract: Most feature screening methods for ultrahigh-dimensional classification explicitly or implicitly assume the covariates are continuous. However, in the practice, it is quite common that both categorical and continuous covariates appear in the data, and applicable feature screening method is very limited. To handle this non-trivial situation, we propose an entropy-based feature screening method, which is model free and provides a unified screening procedure for both categorical and continuous covariates. We establish the sure screening and ranking consistency properties of the proposed procedure. We investigate the finite sample performance of the proposed procedure by simulation studies and illustrate the method by a real data analysis. Journal: Journal of Nonparametric Statistics Pages: 515-530 Issue: 3 Volume: 28 Year: 2016 Month: 9 X-DOI: 10.1080/10485252.2016.1167206 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1167206 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:3:p:515-530 Template-Type: ReDIF-Article 1.0 Author-Name: S. Hossain Author-X-Name-First: S. Author-X-Name-Last: Hossain Author-Name: S. Ejaz Ahmed Author-X-Name-First: S. Ejaz Author-X-Name-Last: Ahmed Author-Name: Grace Y. Yi Author-X-Name-First: Grace Y. Author-X-Name-Last: Yi Author-Name: B. Chen Author-X-Name-First: B. Author-X-Name-Last: Chen Title: Shrinkage and pretest estimators for longitudinal data analysis under partially linear models Abstract: In this paper, we develop marginal analysis methods for longitudinal data under partially linear models. We employ the pretest and shrinkage estimation procedures to estimate the mean response parameters as well as the association parameters, which may be subject to certain restrictions. We provide the analytic expressions for the asymptotic biases and risks of the proposed estimators, and investigate their relative performance to the unrestricted semiparametric least-squares estimator (USLSE). We show that if the dimension of association parameters exceeds two, the risk of the shrinkage estimators is strictly less than that of the USLSE in most of the parameter space. On the other hand, the risk of the pretest estimator depends on the validity of the restrictions of association parameters. A simulation study is conducted to evaluate the performance of the proposed estimators relative to that of the USLSE. A real data example is applied to illustrate the practical usefulness of the proposed estimation procedures. Journal: Journal of Nonparametric Statistics Pages: 531-549 Issue: 3 Volume: 28 Year: 2016 Month: 9 X-DOI: 10.1080/10485252.2016.1190358 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1190358 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:3:p:531-549 Template-Type: ReDIF-Article 1.0 Author-Name: Guy-vanie M. Miakonkana Author-X-Name-First: Guy-vanie M. Author-X-Name-Last: Miakonkana Author-Name: Brice M. Nguelifack Author-X-Name-First: Brice M. Author-X-Name-Last: Nguelifack Author-Name: Asheber Abebe Author-X-Name-First: Asheber Author-X-Name-Last: Abebe Title: Rank-based group variable selection Abstract: A robust rank-based estimator for variable selection in linear models, with grouped predictors, is studied. The proposed estimation procedure extends the existing rank-based variable selection [Johnson, B.A., and Peng, L. (2008), ‘Rank-based Variable Selection’, Journal of Nonparametric Statistics, 20(3):241--252] and the ww-scad [Wang, L., and Li, R. (2009), ‘Weighted Wilcoxon-type Smoothly Clipped Absolute Deviation Method’, Biometrics, 65(2):564--571] to linear regression models with grouped variables. The resulting estimator is robust to contamination or deviations in both the response and the design space.The Oracle property and asymptotic normality of the estimator are established under some regularity conditions. Simulation studies reveal that the proposed method performs better than the existing rank-based methods [Johnson, B.A., and Peng, L. (2008), ‘Rank-based Variable Selection’, Journal of Nonparametric Statistics, 20(3):241--252; Wang, L., and Li, R. (2009), ‘Weighted Wilcoxon-type Smoothly Clipped Absolute Deviation Method’, Biometrics, 65(2):564--571] for grouped variables models. This estimation procedure also outperforms the adaptive hlasso [Zhou, N., and Zhu, J. (2010), ‘Group Variable Selection Via a Hierarchical Lasso and its Oracle Property’, Interface, 3(4):557--574] in the presence of local contamination in the design space or for heavy-tailed error distribution. Journal: Journal of Nonparametric Statistics Pages: 550-562 Issue: 3 Volume: 28 Year: 2016 Month: 9 X-DOI: 10.1080/10485252.2016.1190842 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1190842 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:3:p:550-562 Template-Type: ReDIF-Article 1.0 Author-Name: Zhiyi Zhang Author-X-Name-First: Zhiyi Author-X-Name-Last: Zhang Author-Name: Michael Grabchak Author-X-Name-First: Michael Author-X-Name-Last: Grabchak Title: Entropic representation and estimation of diversity indices Abstract: This paper serves a twofold purpose. First, a unified perspective on diversity indices is introduced based on an entropic basis. It is shown that the class of all linear combinations of the entropic basis, referred to as the class of linear diversity indices, covers a wide range of diversity indices used in the literature. Second, a class of estimators for linear diversity indices is proposed and it is shown that these estimators have rapidly decaying biases and asymptotic normality. Journal: Journal of Nonparametric Statistics Pages: 563-575 Issue: 3 Volume: 28 Year: 2016 Month: 9 X-DOI: 10.1080/10485252.2016.1190357 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1190357 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:3:p:563-575 Template-Type: ReDIF-Article 1.0 Author-Name: Sh. Olimjon Sharipov Author-X-Name-First: Sh. Olimjon Author-X-Name-Last: Sharipov Author-Name: Johannes Tewes Author-X-Name-First: Johannes Author-X-Name-Last: Tewes Author-Name: Martin Wendler Author-X-Name-First: Martin Author-X-Name-Last: Wendler Title: Bootstrap for U-statistics: a new approach Abstract: Bootstrap for nonlinear statistics like U-statistics of dependent data has been studied by several authors. This is typically done by producing a bootstrap version of the sample and plugging it into the statistic. We suggest an alternative approach of getting a bootstrap version of U-statistics. We will show the consistency of the new method and compare its finite sample properties in a simulation study and by applying both methods to financial data. Journal: Journal of Nonparametric Statistics Pages: 576-594 Issue: 3 Volume: 28 Year: 2016 Month: 9 X-DOI: 10.1080/10485252.2016.1190843 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1190843 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:3:p:576-594 Template-Type: ReDIF-Article 1.0 Author-Name: Miao Yang Author-X-Name-First: Miao Author-X-Name-Last: Yang Author-Name: Lan Xue Author-X-Name-First: Lan Author-X-Name-Last: Xue Author-Name: Lijian Yang Author-X-Name-First: Lijian Author-X-Name-Last: Yang Title: Variable selection for additive model via cumulative ratios of empirical strengths total Abstract: We propose a data-driven method to select significant variables in additive model via spline estimation. The additive structure of the regression model is imposed to overcome the ‘curse of dimensionality’, while the spline estimators provide a good approximation to the additive components of the model. The additive components are ordered according to their empirical strengths, and the significant variables are chosen at the first crossing of a predetermined threshold by the CUmulative Ratios of Empirical Strengths Total of the components. Consistency of the proposed method is established when the number of variables are allowed to diverge with sample size, while extensive Monte-Carlo study demonstrates superior performance of the proposed method and its advantages over the BIC method of Huang and Yang [(2004), ‘Identification of Nonlinear: Additive Autoregressive Models’, Journal of the Royal Statistical Society Series B, 66, 463--477] in terms of speed and accuracy. Journal: Journal of Nonparametric Statistics Pages: 595-616 Issue: 3 Volume: 28 Year: 2016 Month: 9 X-DOI: 10.1080/10485252.2016.1191633 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1191633 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:3:p:595-616 Template-Type: ReDIF-Article 1.0 Author-Name: Cunjie Lin Author-X-Name-First: Cunjie Author-X-Name-Last: Lin Author-Name: Li Zhang Author-X-Name-First: Li Author-X-Name-Last: Zhang Author-Name: Yong Zhou Author-X-Name-First: Yong Author-X-Name-Last: Zhou Title: Inference on quantile residual life function under right-censored data Abstract: The quantile residual lifetime function is a comprehensive quantitative description of a residual lifetime. Under the assumption of independent censoring, a naive estimator for the quantile residual lifetime function can be obtained by inverting the Kaplan--Meier estimator. However, this naive estimator is biased when survival and censoring times are dependent. In this paper, we propose a method for estimating the quantile residual lifetime function, taking into account the covariates and relaxing the assumption of independent censoring. To compare two quantile residual lifetime functions at fixed time points, we construct two test statistics which are easy to implement. We also derive the asymptotic properties for the proposed estimator and test statistics. A re-sampling method for estimating the asymptotic variance of the proposed estimator is provided. Simulation studies are conducted to assess the finite sample properties of the estimator and the performance of the test statistics. We also apply the proposed method to the real data and report some interesting results. Journal: Journal of Nonparametric Statistics Pages: 617-643 Issue: 3 Volume: 28 Year: 2016 Month: 9 X-DOI: 10.1080/10485252.2016.1190841 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1190841 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:3:p:617-643 Template-Type: ReDIF-Article 1.0 Author-Name: Hongmei Lin Author-X-Name-First: Hongmei Author-X-Name-Last: Lin Author-Name: Riquan Zhang Author-X-Name-First: Riquan Author-X-Name-Last: Zhang Author-Name: Jianhong Shi Author-X-Name-First: Jianhong Author-X-Name-Last: Shi Author-Name: Jicai Liu Author-X-Name-First: Jicai Author-X-Name-Last: Liu Author-Name: Yanghui Liu Author-X-Name-First: Yanghui Author-X-Name-Last: Liu Title: A new local estimation method for single index models for longitudinal data Abstract: Single index models are natural extensions of linear models and overcome the so-called curse of dimensionality. They are very useful for longitudinal data analysis. In this paper, we develop a new efficient estimation procedure for single index models with longitudinal data, based on Cholesky decomposition and local linear smoothing method. Asymptotic normality for the proposed estimators of both the parametric and nonparametric parts will be established. Monte Carlo simulation studies show excellent finite sample performance. Furthermore, we illustrate our methods with a real data example. Journal: Journal of Nonparametric Statistics Pages: 644-658 Issue: 3 Volume: 28 Year: 2016 Month: 9 X-DOI: 10.1080/10485252.2016.1191632 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1191632 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:3:p:644-658 Template-Type: ReDIF-Article 1.0 Author-Name: David Lee Author-X-Name-First: David Author-X-Name-Last: Lee Author-Name: Harry Joe Author-X-Name-First: Harry Author-X-Name-Last: Joe Author-Name: Pavel Krupskii Author-X-Name-First: Pavel Author-X-Name-Last: Krupskii Title: Tail-weighted dependence measures with limit being the tail dependence coefficient Abstract: For bivariate continuous data, measures of monotonic dependence are based on the rank transformations of the two variables. For bivariate extreme value copulas, there is a family of estimators $ {\hat \vartheta }_\alpha $ ϑˆα, for $ \alpha >0 $ α>0, of the extremal coefficient, based on a transform of the absolute difference of the α power of the ranks. In the case of general bivariate copulas, we obtain the probability limit $ \zeta _\alpha $ ζα of $ \hat {\zeta }_\alpha =2-{\hat \vartheta }_\alpha $ ζˆα=2−ϑˆα as the sample size goes to infinity and show that (i) $ \zeta _\alpha $ ζα for $ \alpha =1 $ α=1 is a measure of central dependence with properties similar to Kendall's tau and Spearman's rank correlation, (ii) $ \zeta _\alpha $ ζα is a tail-weighted dependence measure for large α, and (iii) the limit as $ \alpha \to \infty $ α→∞ is the upper tail dependence coefficient. We obtain asymptotic properties for the rank-based measure $ {\hat \zeta }_\alpha $ ζˆα and estimate tail dependence coefficients through extrapolation on $ {\hat \zeta }_\alpha $ ζˆα. A data example illustrates the use of the new dependence measures for tail inference. Journal: Journal of Nonparametric Statistics Pages: 262-290 Issue: 2 Volume: 30 Year: 2018 Month: 4 X-DOI: 10.1080/10485252.2017.1407414 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1407414 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:2:p:262-290 Template-Type: ReDIF-Article 1.0 Author-Name: Yu-Ning Li Author-X-Name-First: Yu-Ning Author-X-Name-Last: Li Author-Name: Yi Zhang Author-X-Name-First: Yi Author-X-Name-Last: Zhang Title: Estimation of heteroscedasticity by local composite quantile regression and matrix decomposition Abstract: We propose a two-step estimation method for nonparametric model with heteroscedasticity to estimate the scale function $ \sigma (\cdot ) $ σ(⋅) and the location function $ m(\cdot ) $ m(⋅) simultaneously. The local composite quantile regression (LCQR) is employed in the first step, and a matrix decomposition method is used to estimate both $ m(\cdot ) $ m(⋅) and $ \sigma (\cdot ) $ σ(⋅) in the second step. We prove the non-crossing property of the LCQR and thereby give an algorithm, named matrix decomposition method, to ensure the non-negativity of the scale function estimator, which is much reasonable since there is no hard constraint or order adjustment to the estimators. Under some mild regularity conditions, the resulting estimator enjoys asymptotic normality. Simulation results demonstrate that a better estimator of the scale function can be obtained in terms of mean square error, no matter the error distribution is symmetric or not. Finally, a real data example is used to illustrate the proposed method. Journal: Journal of Nonparametric Statistics Pages: 291-307 Issue: 2 Volume: 30 Year: 2018 Month: 4 X-DOI: 10.1080/10485252.2017.1418869 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1418869 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:2:p:291-307 Template-Type: ReDIF-Article 1.0 Author-Name: Junyi Zhang Author-X-Name-First: Junyi Author-X-Name-Last: Zhang Author-Name: Zhezhen Jin Author-X-Name-First: Zhezhen Author-X-Name-Last: Jin Author-Name: Yongzhao Shao Author-X-Name-First: Yongzhao Author-X-Name-Last: Shao Author-Name: Zhiliang Ying Author-X-Name-First: Zhiliang Author-X-Name-Last: Ying Title: Statistical inference on transformation models: a self-induced smoothing approach Abstract: This paper deals with a general class of transformation models that contains many important semiparametric regression models as special cases. It develops a self-induced smoothing for the maximum rank correlation estimator, resulting in simultaneous point and variance estimation. The self-induced smoothing does not require bandwidth selection, yet provides the right amount of smoothness so that the estimator is asymptotically normal with mean zero (unbiased) and variance–covariance matrix consistently estimated by the usual sandwich-type estimator. An iterative algorithm is given for the variance estimation and shown to numerically converge to a consistent limiting variance estimator. The approach is applied to a data set involving survival times of primary biliary cirrhosis patients. Simulation results are reported, showing that the new method performs well under a variety of scenarios. Journal: Journal of Nonparametric Statistics Pages: 308-331 Issue: 2 Volume: 30 Year: 2018 Month: 4 X-DOI: 10.1080/10485252.2018.1424334 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1424334 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:2:p:308-331 Template-Type: ReDIF-Article 1.0 Author-Name: Wenhua Wei Author-X-Name-First: Wenhua Author-X-Name-Last: Wei Author-Name: Alan T. K. Wan Author-X-Name-First: Alan T. K. Author-X-Name-Last: Wan Author-Name: Yong Zhou Author-X-Name-First: Yong Author-X-Name-Last: Zhou Title: Partially linear transformation model for length-biased and right-censored data Abstract: In this paper, we consider a partially linear transformation model for data subject to length-biasedness and right-censoring which frequently arise simultaneously in biometrics and other fields. The partially linear transformation model can account for nonlinear covariate effects in addition to linear effects on survival time, and thus reconciles a major disadvantage of the popular semiparamnetric linear transformation model. We adopt local linear fitting technique and develop an unbiased global and local estimating equations approach for the estimation of unknown covariate effects. We provide an asymptotic justification for the proposed procedure, and develop an iterative computational algorithm for its practical implementation, and a bootstrap resampling procedure for estimating the standard errors of the estimator. A simulation study shows that the proposed method performs well in finite samples, and the proposed estimator is applied to analyse the Oscar data. Journal: Journal of Nonparametric Statistics Pages: 332-367 Issue: 2 Volume: 30 Year: 2018 Month: 4 X-DOI: 10.1080/10485252.2018.1424335 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1424335 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:2:p:332-367 Template-Type: ReDIF-Article 1.0 Author-Name: J. P. Florens Author-X-Name-First: J. P. Author-X-Name-Last: Florens Author-Name: J. S. Racine Author-X-Name-First: J. S. Author-X-Name-Last: Racine Author-Name: S. Centorrino Author-X-Name-First: S. Author-X-Name-Last: Centorrino Title: Nonparametric instrumental variable derivative estimation Abstract: The focus of this paper is the nonparametric estimation of the marginal effects (i.e. first partial derivatives) of an instrumental regression function ϕ defined by conditional moment restrictions that stem from a structural econometric model $ E[Y-\varphi (Z)\,|\,W]=0 $ E[Y−ϕ(Z)|W]=0, and involve endogenous variables Y and Z and instruments W. The derivative function $ \varphi ' $ ϕ′ is the solution of an ill-posed inverse problem and we propose an estimation procedure based on Landweber–Fridman regularisation. We provide theoretical underpinnings of the proposed approach, examine finite-sample performance, and consider an illustrative application. Journal: Journal of Nonparametric Statistics Pages: 368-391 Issue: 2 Volume: 30 Year: 2018 Month: 4 X-DOI: 10.1080/10485252.2018.1428745 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1428745 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:2:p:368-391 Template-Type: ReDIF-Article 1.0 Author-Name: Anton Schick Author-X-Name-First: Anton Author-X-Name-Last: Schick Author-Name: Yilin Zhu Author-X-Name-First: Yilin Author-X-Name-Last: Zhu Author-Name: Xiaojie Du Author-X-Name-First: Xiaojie Author-X-Name-Last: Du Title: Estimation of the error distribution in a varying coefficient regression model Abstract: This paper deals with the estimation of the error distribution function in a varying coefficient regression model. We propose two estimators and study their asymptotic properties by obtaining uniform stochastic expansions. The first estimator is a residual-based empirical distribution function. We study this estimator when the varying coefficients are estimated by under-smoothed local quadratic smoothers. Our second estimator which exploits the fact that the error distribution has mean zero is a weighted residual-based empirical distribution whose weights are chosen to achieve the mean zero property using empirical likelihood methods. The second estimator improves on the first estimator. Bootstrap confidence bands based on the two estimators are also discussed. Journal: Journal of Nonparametric Statistics Pages: 392-429 Issue: 2 Volume: 30 Year: 2018 Month: 4 X-DOI: 10.1080/10485252.2018.1429608 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1429608 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:2:p:392-429 Template-Type: ReDIF-Article 1.0 Author-Name: Lei Huo Author-X-Name-First: Lei Author-X-Name-Last: Huo Author-Name: Xuerong Meggie Wen Author-X-Name-First: Xuerong Meggie Author-X-Name-Last: Wen Author-Name: Zhou Yu Author-X-Name-First: Zhou Author-X-Name-Last: Yu Title: Trace pursuit variable selection for multi-population data Abstract: Variable selection is a very important tool when dealing with high dimensional data. However, most popular variable selection methods are model based, which might provide misleading results when the model assumption is not satisfied. Sufficient dimension reduction provides a general framework for model-free variable selection methods. In this paper, we propose a model-free variable selection method via sufficient dimension reduction, which incorporates the grouping information into the selection procedure for multi-population data. Theoretical properties of our selection methods are also discussed. Simulation studies suggest that our method greatly outperforms those ignoring the grouping information. Journal: Journal of Nonparametric Statistics Pages: 430-447 Issue: 2 Volume: 30 Year: 2018 Month: 4 X-DOI: 10.1080/10485252.2018.1430364 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1430364 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:2:p:430-447 Template-Type: ReDIF-Article 1.0 Author-Name: Ery Arias-Castro Author-X-Name-First: Ery Author-X-Name-Last: Arias-Castro Author-Name: Bruno Pelletier Author-X-Name-First: Bruno Author-X-Name-Last: Pelletier Author-Name: Venkatesh Saligrama Author-X-Name-First: Venkatesh Author-X-Name-Last: Saligrama Title: Remember the curse of dimensionality: the case of goodness-of-fit testing in arbitrary dimension Abstract: Despite a substantial literature on nonparametric two-sample goodness-of-fit testing in arbitrary dimensions, there is no mention there of any curse of dimensionality. In fact, in some publications, a parametric rate is derived. As we discuss below, this is because a directional alternative is considered. Indeed, even in dimension one, Ingster, Y. I. [(1987). Minimax testing of nonparametric hypotheses on a distribution density in the l_p metrics. Theory of Probability & Its Applications, 31(2), 333–337] has shown that the minimax rate is not parametric. In this paper, we extend his results to arbitrary dimension and confirm that the minimax rate is not only nonparametric, exhibits but also a prototypical curse of dimensionality. We further extend Ingster's work to show that the chi-squared test achieves the minimax rate. Moreover, we show that the test adapts to the intrinsic dimensionality of the data. Finally, in the spirit of Ingster, Y. I. [(2000). Adaptive chi-square tests. Journal of Mathematical Sciences, 99(2), 1110–1119], we consider a multiscale version of the chi-square test, showing that one can adapt to unknown smoothness without much loss in power. Journal: Journal of Nonparametric Statistics Pages: 448-471 Issue: 2 Volume: 30 Year: 2018 Month: 4 X-DOI: 10.1080/10485252.2018.1435875 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1435875 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:2:p:448-471 Template-Type: ReDIF-Article 1.0 Author-Name: Belkais Altendji Author-X-Name-First: Belkais Author-X-Name-Last: Altendji Author-Name: Jacques Demongeot Author-X-Name-First: Jacques Author-X-Name-Last: Demongeot Author-Name: Ali Laksaci Author-X-Name-First: Ali Author-X-Name-Last: Laksaci Author-Name: Mustapha Rachdi Author-X-Name-First: Mustapha Author-X-Name-Last: Rachdi Title: Functional data analysis: estimation of the relative error in functional regression under random left-truncation model Abstract: In this paper, we investigate the relationship between a functional random covariable and a scalar response which is subject to left-truncation by another random variable. Precisely, we use the mean squared relative error as a loss function to construct a nonparametric estimator of the regression operator of these functional truncated data. Under some standard assumptions in functional data analysis, we establish the almost sure consistency, with rates, of the constructed estimator as well as its asymptotic normality. Then, a simulation study, on finite-sized samples, was carried out in order to show the efficiency of our estimation procedure and to highlight its superiority over the classical kernel estimation, for different levels of simulated truncated data. Journal: Journal of Nonparametric Statistics Pages: 472-490 Issue: 2 Volume: 30 Year: 2018 Month: 4 X-DOI: 10.1080/10485252.2018.1438609 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1438609 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:2:p:472-490 Template-Type: ReDIF-Article 1.0 Author-Name: Ying Zhang Author-X-Name-First: Ying Author-X-Name-Last: Zhang Author-Name: Lei Wang Author-X-Name-First: Lei Author-X-Name-Last: Wang Title: Dimension reduction in estimating equations with covariates missing at random Abstract: To estimate parameters defined by estimating equations with covariates missing at random, we consider three bias-corrected nonparametric approaches based on inverse probability weighting, regression and augmented inverse probability weighting. However, when the dimension of covariates is not low, the estimation efficiency will be affected due to the curse of dimensionality. To address this issue, we propose a two-stage estimation procedure by using the dimension-reduced kernel estimation in conjunction with bias-corrected estimating equations. We show that the resulting three estimators are asymptotically equivalent and achieve the desirable properties. The impact of dimension reduction in nonparametric estimation of parameters is also investigated. The finite-sample performance of the proposed estimators is studied through simulation, and an application to an automobile data set is also presented. Journal: Journal of Nonparametric Statistics Pages: 491-504 Issue: 2 Volume: 30 Year: 2018 Month: 4 X-DOI: 10.1080/10485252.2018.1438610 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1438610 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:2:p:491-504 Template-Type: ReDIF-Article 1.0 Author-Name: Yousri Slaoui Author-X-Name-First: Yousri Author-X-Name-Last: Slaoui Title: Bias reduction in kernel density estimation Abstract: In this paper, we propose two kernel density estimators based on a bias reduction technique. We study the properties of these estimators and compare them with Parzen–Rosenblatt's density estimator and Mokkadem, A., Pelletier, M., and Slaoui, Y. (2009, ‘The stochastic approximation method for the estimation of a multivariate probability density’, J. Statist. Plann. Inference, 139, 2459–2478) is density estimators. It turns out that, with an adequate choice of the parameters of the two proposed estimators, the rate of convergence of two estimators will be faster than the two classical estimators and the asymptotic MISE (Mean Integrated Squared Error) will be smaller than the two classical estimators. We corroborate these theoretical results through simulations. Journal: Journal of Nonparametric Statistics Pages: 505-522 Issue: 2 Volume: 30 Year: 2018 Month: 4 X-DOI: 10.1080/10485252.2018.1442927 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1442927 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:2:p:505-522 Template-Type: ReDIF-Article 1.0 Author-Name: Ioannis S. Triantafyllou Author-X-Name-First: Ioannis S. Author-X-Name-Last: Triantafyllou Title: A new distribution-free control scheme based on order statistics Abstract: We establish a class of nonparametric Shewhart-type control charts based on a reference sample drawn from the process. The proposed nonparametric control chart takes advantage of the location of two different order statistics of the reference and test sample respectively. The decision rule of the new monitoring scheme is filled out by the number of test observations that are located between the control limits. The general setup of the new class of control charts is presented in detail, while the operating characteristic function is studied for both in- and out-of-control processes. Closed formulae for the evaluation of the alarm rate and the average run length are concluded for plausible shift in the underlying distribution to Lehmann alternatives. Several numerical results, displayed for the new family of nonparametric control charts, depict that the proposed control scheme attains competitive performance. Journal: Journal of Nonparametric Statistics Pages: 1-30 Issue: 1 Volume: 31 Year: 2019 Month: 1 X-DOI: 10.1080/10485252.2018.1518524 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1518524 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:1:p:1-30 Template-Type: ReDIF-Article 1.0 Author-Name: Chrysoula Dimitriou-Fakalou Author-X-Name-First: Chrysoula Author-X-Name-Last: Dimitriou-Fakalou Title: The table auto-regressive moving-average model for (categorical) stationary series: statistical properties (causality; from the all random to the conditional random) Abstract: A strictly stationary time series is modelled directly, once the variables' realizations fit into a table: no knowledge of a distribution is required other than the prior discretization. A multiplicative model with combined random ‘Auto-Regressive’ and ‘Moving-Average’ parts is considered for the serial dependence. Based on a multi-sequence of unobserved series that serve as differences and differences of differences from the main building block, a causal version is obtained; a condition that secures an exponential rate of convergence for its expected random coefficients is presented. For the remainder, writing the conditional probability as a function of past conditional probabilities, is within reach: subject to the presence of the moving-average segment in the original equation, what could be a long process of elimination with mathematical arguments concludes with a new derivation that does not support a simplistic linear dependence on the lagged probability values. Journal: Journal of Nonparametric Statistics Pages: 31-63 Issue: 1 Volume: 31 Year: 2019 Month: 1 X-DOI: 10.1080/10485252.2018.1527912 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1527912 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:1:p:31-63 Template-Type: ReDIF-Article 1.0 Author-Name: Guangbao Guo Author-X-Name-First: Guangbao Author-X-Name-Last: Guo Author-Name: James Allison Author-X-Name-First: James Author-X-Name-Last: Allison Author-Name: Lixing Zhu Author-X-Name-First: Lixing Author-X-Name-Last: Zhu Title: Bootstrap maximum likelihood for quasi-stationary distributions Abstract: Quasi-stationary distributions have many applications in diverse research fields. We develop a bootstrap-based maximum likelihood (BML) method to deal with quasi-stationary distributions in statistical inference. To efficiently implement a bootstrap procedure that can handle the dependence among observations and speed up the computation, a novel block bootstrap algorithm is proposed to accommodate parallel bootstrap. In particular, we select a suitable block length for use with the parallel bootstrap. The estimation error is investigated to show its convergence. The proposed BML is shown to be asymptotically unbiased. Some numerical studies are given to examine the performance of the new algorithm. The advantages are evidenced through a comparison with some competitors and some examples are analysed for illustration. Journal: Journal of Nonparametric Statistics Pages: 64-87 Issue: 1 Volume: 31 Year: 2019 Month: 1 X-DOI: 10.1080/10485252.2018.1531130 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1531130 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:1:p:64-87 Template-Type: ReDIF-Article 1.0 Author-Name: Hadi Alizadeh Noughabi Author-X-Name-First: Hadi Author-X-Name-Last: Alizadeh Noughabi Author-Name: Jalil Jarrahiferiz Author-X-Name-First: Jalil Author-X-Name-Last: Jarrahiferiz Title: On the estimation of extropy Abstract: Recently, Lad, Sanfilippo, and Agro [(2015), ‘Extropy: Complementary Dual of Entropy’, Statistical Science, 30, 40–58.] showed the measure of entropy has a complementary dual, which is termed extropy. The present article introduces some estimators of the extropy of a continuous random variable. Properties of the proposed estimators are stated, and comparisons are made with Qiu and Jia’s estimators [(2018a), ‘Extropy Estimators with Applications in Testing uniformity’, Journal of Nonparametric Statistics, 30, 182–196]. The results indicate that the proposed estimators have a smaller mean squared error than competing estimators. A real example is presented and analysed. Journal: Journal of Nonparametric Statistics Pages: 88-99 Issue: 1 Volume: 31 Year: 2019 Month: 1 X-DOI: 10.1080/10485252.2018.1533133 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1533133 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:1:p:88-99 Template-Type: ReDIF-Article 1.0 Author-Name: Robert P. Lieli Author-X-Name-First: Robert P. Author-X-Name-Last: Lieli Author-Name: Yu-Chin Hsu Author-X-Name-First: Yu-Chin Author-X-Name-Last: Hsu Title: Using the area under an estimated ROC curve to test the adequacy of binary predictors Abstract: We consider using the area under an empirical receiver operating characteristic curve to test the hypothesis that a predictive index combined with a range of cutoffs performs no better than pure chance in forecasting a binary outcome. This corresponds to the null hypothesis that the area in question, denoted as AUC, is 1/2. We show that if the predictive index comes from a first-stage regression model estimated over the same data set, then testing the null based on the standard asymptotic normality results leads to severe size distortion in general settings. We then analytically derive the proper asymptotic null distribution of the empirical AUC in a special case; namely, when the first-stage regressors are Bernoulli random variables. This distribution can be utilised to construct a fully in-sample test of $ H_0: {\rm AUC}=1/2 $ H0:AUC=1/2 with correct size and more power than out-of-sample tests based on sample splitting, though practical application becomes cumbersome with more than two regressors. Journal: Journal of Nonparametric Statistics Pages: 100-130 Issue: 1 Volume: 31 Year: 2019 Month: 1 X-DOI: 10.1080/10485252.2018.1537440 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1537440 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:1:p:100-130 Template-Type: ReDIF-Article 1.0 Author-Name: Hailin Huang Author-X-Name-First: Hailin Author-X-Name-Last: Huang Author-Name: Yanlin Tang Author-X-Name-First: Yanlin Author-X-Name-Last: Tang Author-Name: Yuanzhang Li Author-X-Name-First: Yuanzhang Author-X-Name-Last: Li Author-Name: Hua Liang Author-X-Name-First: Hua Author-X-Name-Last: Liang Title: Estimation in additive models with fixed censored responses Abstract: We propose a new estimation method to estimate the nonparametric functions in additive models, where the response is subject to fixed censoring. Under some regularity conditions, we show that the proposed estimator is uniformly consistent with certain convergence rates. The simulation study shows that the proposed estimator performs well in finite sample sizes. We also analyze a dataset from an HIV study for an illustration. Journal: Journal of Nonparametric Statistics Pages: 131-143 Issue: 1 Volume: 31 Year: 2019 Month: 1 X-DOI: 10.1080/10485252.2018.1537441 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1537441 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:1:p:131-143 Template-Type: ReDIF-Article 1.0 Author-Name: B. Béranger Author-X-Name-First: B. Author-X-Name-Last: Béranger Author-Name: T. Duong Author-X-Name-First: T. Author-X-Name-Last: Duong Author-Name: S. E. Perkins-Kirkpatrick Author-X-Name-First: S. E. Author-X-Name-Last: Perkins-Kirkpatrick Author-Name: S. A. Sisson Author-X-Name-First: S. A. Author-X-Name-Last: Sisson Title: Tail density estimation for exploratory data analysis using kernel methods Abstract: It is often critical to accurately model the upper tail behaviour of a random process. Nonparametric density estimation methods are commonly implemented as exploratory data analysis techniques for this purpose and can avoid model specification biases implied by using parametric estimators. In particular, kernel-based estimators place minimal assumptions on the data, and provide improved visualisation over scatterplots and histograms. However kernel density estimators can perform poorly when estimating tail behaviour above a threshold, and can over-emphasise bumps in the density for heavy tailed data. We develop a transformation kernel density estimator which is able to handle heavy tailed and bounded data, and is robust to threshold choice. We derive closed form expressions for its asymptotic bias and variance, which demonstrate its good performance in the tail region. Finite sample performance is illustrated in numerical studies, and in an expanded analysis of the performance of global climate models. Journal: Journal of Nonparametric Statistics Pages: 144-174 Issue: 1 Volume: 31 Year: 2019 Month: 1 X-DOI: 10.1080/10485252.2018.1537442 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1537442 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:1:p:144-174 Template-Type: ReDIF-Article 1.0 Author-Name: Zouaoui Chikr-Elmezouar Author-X-Name-First: Zouaoui Author-X-Name-Last: Chikr-Elmezouar Author-Name: Ibrahim M. Almanjahie Author-X-Name-First: Ibrahim M. Author-X-Name-Last: Almanjahie Author-Name: Ali Laksaci Author-X-Name-First: Ali Author-X-Name-Last: Laksaci Author-Name: Mustapha Rachdi Author-X-Name-First: Mustapha Author-X-Name-Last: Rachdi Title: FDA: strong consistency of the NN local linear estimation of the functional conditional density and mode Abstract: In this paper we present a new estimator of the conditional density and mode when the co-variables are of functional kind. This estimator is a combination of both, the k-Nearest Neighbours procedure and the functional local linear estimation. Then, for each statistical parameter (conditional density or mode), results concerning the strong consistency and rate of convergence of the estimators are presented. Finally, their performances, for finite sample sizes, are illustrated by using simulated data. Journal: Journal of Nonparametric Statistics Pages: 175-195 Issue: 1 Volume: 31 Year: 2019 Month: 1 X-DOI: 10.1080/10485252.2018.1538450 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1538450 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:1:p:175-195 Template-Type: ReDIF-Article 1.0 Author-Name: Xiao Song Author-X-Name-First: Xiao Author-X-Name-Last: Song Author-Name: Li Wang Author-X-Name-First: Li Author-X-Name-Last: Wang Author-Name: Shuangge Ma Author-X-Name-First: Shuangge Author-X-Name-Last: Ma Author-Name: Hanwen Huang Author-X-Name-First: Hanwen Author-X-Name-Last: Huang Title: Variable selection for partially linear proportional hazards model with covariate measurement error Abstract: In survival analysis, we may encounter the following three problems: nonlinear covariate effect, variable selection and measurement error. Existing studies only address one or two of these problems. The goal of this study is to fill the knowledge gap and develop a novel approach to simultaneously address all three problems. Specifically, a partially time-varying coefficient proportional hazards model is proposed to more flexibly describe covariate effects. Corrected score and conditional score approaches are employed to accommodate potential measurement error. For the selection of relevant variables and regularised estimation, a penalisation approach is adopted. It is shown that the proposed approach has satisfactory asymptotic properties. It can be effectively realised using an iterative algorithm. The performance of the proposed approach is assessed via simulation studies and further illustrated by application to data from an AIDS clinical trial. Journal: Journal of Nonparametric Statistics Pages: 196-220 Issue: 1 Volume: 31 Year: 2019 Month: 1 X-DOI: 10.1080/10485252.2018.1545903 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1545903 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:1:p:196-220 Template-Type: ReDIF-Article 1.0 Author-Name: L. Aït Hennani Author-X-Name-First: L. Author-X-Name-Last: Aït Hennani Author-Name: M. Lemdani Author-X-Name-First: M. Author-X-Name-Last: Lemdani Author-Name: E. Ould Saïd Author-X-Name-First: E. Author-X-Name-Last: Ould Saïd Title: Robust regression analysis for a censored response and functional regressors Abstract: Let $ (T_n)_{ n \geq 1} $ (Tn)n≥1 be an independent and identically distributed (iid) sequence of interest random variables (rv) distributed as T. In censorship models, T is subject to random censoring by another rv C. Based on the so-called synthetic data, we define an M-estimator for the regression function of T given a functional covariate $ {\boldsymbol {\chi }} $ χ. Under standard assumptions on the kernel, bandwidth and small ball probabilities, we establish its strong consistency with rate and asymptotic normality. The asymptotic variance is given explicitly. Confidence bands are given and special cases are studied to show the generality of our work. Finally simulations are drawn to illustrate both quality of fit and robustness. Journal: Journal of Nonparametric Statistics Pages: 221-243 Issue: 1 Volume: 31 Year: 2019 Month: 1 X-DOI: 10.1080/10485252.2018.1546386 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1546386 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:1:p:221-243 Template-Type: ReDIF-Article 1.0 Author-Name: Y. Xiong Author-X-Name-First: Y. Author-X-Name-Last: Xiong Author-Name: D. Bingham Author-X-Name-First: D. Author-X-Name-Last: Bingham Author-Name: W. J. Braun Author-X-Name-First: W. J. Author-X-Name-Last: Braun Author-Name: X. J. Hu Author-X-Name-First: X. J. Author-X-Name-Last: Hu Title: Moran's statistic-based nonparametric test with spatio-temporal observations Abstract: Moran's I statistic [Moran, (1950), ‘Notes on Continuous Stochastic Phenomena’, Biometrika, 37, 17–23] has been widely used to evaluate spatial autocorrelation. This paper is concerned with Moran's I-induced testing procedure in residual analysis. We begin with exploring the Moran's I statistic in both its original and extended forms analytically and numerically. We demonstrate that the magnitude of the statistic in general depends not only on the underlying correlation but also on certain heterogeneity in the individual observations. One should exercise caution when interpreting the outcome on correlation by the Moran's I-induced procedure. On the other hand, the effect on the Moran's I due to heterogeneity in the observations enables a regression model checking procedure with the residuals. This novel application of Moran's I is justified by simulation and illustrated by an analysis of wildfire records from Alberta, Canada. Journal: Journal of Nonparametric Statistics Pages: 244-267 Issue: 1 Volume: 31 Year: 2019 Month: 1 X-DOI: 10.1080/10485252.2018.1550197 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1550197 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:1:p:244-267 Template-Type: ReDIF-Article 1.0 Author-Name: Jørgen Harmse Author-X-Name-First: Jørgen Author-X-Name-Last: Harmse Title: Reduction of Gaussian mixture models by maximum similarity Abstract: Scott and Szewczyk developed an iterative method to simplify (reduce the order of) a Gaussian mixture model by merging the two most similar components. Since the comparison of all pairs of components may not be feasible, they propose to consider only nearly adjacent components, with no guarantee that they find the most similar. I give a method to find the most similar pair of components without comparing all pairs, and I propose an extension to higher dimensions. Journal: Journal of Nonparametric Statistics Pages: 703-709 Issue: 6 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903377293 File-URL: http://hdl.handle.net/10.1080/10485250903377293 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:6:p:703-709 Template-Type: ReDIF-Article 1.0 Author-Name: Clément Marteau Author-X-Name-First: Clément Author-X-Name-Last: Marteau Title: The Stein hull Abstract: We are interested in the statistical linear inverse problem Y=Af+εξ, where A denotes a compact operator and εξ a stochastic noise. In this setting, the risk hull point of view provides interesting tools for the construction of adaptive estimators. It sheds light on the processes governing the behaviour of linear estimators. In this article, we investigate the link between some threshold estimators and this risk hull point of view. The penalised blockwise Stein rule plays a central role in this study. In particular, this estimator may be considered as a risk hull minimisation method, provided the penalty is well chosen. Using this perspective, we study the properties of the threshold and propose an admissible range for the penalty leading to accurate results. We eventually propose a penalty close to the lower bound of this range. Journal: Journal of Nonparametric Statistics Pages: 685-702 Issue: 6 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903388878 File-URL: http://hdl.handle.net/10.1080/10485250903388878 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:6:p:685-702 Template-Type: ReDIF-Article 1.0 Author-Name: A. Mosamam Author-X-Name-First: A. Author-X-Name-Last: Mosamam Author-Name: J. Kent Author-X-Name-First: J. Author-X-Name-Last: Kent Title: Semi-reproducing kernel Hilbert spaces, splines and increment kriging Abstract: A reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions on an index set E, say, for which function evaluation is continuous in the Hilbert norm. One of the classic applications of such spaces is to show that the solution of a certain penalised least squares problem is given by a smoothing spline. However, the formulation of this problem in an RKHS setting involves several arbitrary choices. In this paper, we propose the use of a semi-RKHS (SRKHS), which provides a more natural setting for the smoothing spline solution. In addition, a systematic study is made of the properties of an SRKHS. It is well known that there is a one-to-one correspondence between an RKHS and positive semi-definite (psd) function on E, which in turn can be viewed as the covariance function of a stochastic process on E. In this paper, we extend this result to show that there is a one-to-one correspondence between an SRKHS and conditionally positive semi-definite (cpsd) function on E, which in turn defines the covariance behaviour of certain increments on E. Further, it is shown how optimal smoothing in the functional setting corresponds to optimal prediction in the stochastic process setting. Journal: Journal of Nonparametric Statistics Pages: 711-722 Issue: 6 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903388886 File-URL: http://hdl.handle.net/10.1080/10485250903388886 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:6:p:711-722 Template-Type: ReDIF-Article 1.0 Author-Name: Holger Dette Author-X-Name-First: Holger Author-X-Name-Last: Dette Author-Name: Mareen Marchlewski Author-X-Name-First: Mareen Author-X-Name-Last: Marchlewski Title: A robust test for homoscedasticity in nonparametric regression Abstract: We consider a nonparametric location scale model and propose a new test for homoscedasticity (constant scale function). The test is based on an estimate of a deterministic function that vanishes if and only if the hypothesis of a constant scale function is satisfied and an empirical process estimating this function is investigated. Weak convergence to a scaled Brownian bridge is established, which allows a simple calculation of critical values. The new test can detect alternatives converging to the null hypothesis at a rate n−1/2 and is robust with respect to the presence of outliers. The finite sample properties are investigated by means of a simulation study, and the test is compared with some nonrobust tests for a constant scale function, which have recently been proposed in the literature. Journal: Journal of Nonparametric Statistics Pages: 723-736 Issue: 6 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903388894 File-URL: http://hdl.handle.net/10.1080/10485250903388894 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:6:p:723-736 Template-Type: ReDIF-Article 1.0 Author-Name: Tao Hu Author-X-Name-First: Tao Author-X-Name-Last: Hu Author-Name: Hengjian Cui Author-X-Name-First: Hengjian Author-X-Name-Last: Cui Title: Robust estimates in generalised varying-coefficient partially linear models Abstract: In this article, we introduce a family of robust estimates for the parametric and nonparametric components under a generalised semiparametric varying coefficient partially linear regression model, where the data are modelled by yi|(xi, zi, ui) ∼ F (·, μi) with for some known distribution function F and link function H. A class of sieve robust estimation is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent; the convergence rate of the estimator for the unknown nonparametric component is obtained and the estimator for the unknown parameter is shown to be asymptotically normally distributed. Four simulation studies are conducted to examine the small-sample properties of the proposed estimates and a real data set is used to illustrate our approach. Journal: Journal of Nonparametric Statistics Pages: 737-754 Issue: 6 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903428468 File-URL: http://hdl.handle.net/10.1080/10485250903428468 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:6:p:737-754 Template-Type: ReDIF-Article 1.0 Author-Name: Denis Larocque Author-X-Name-First: Denis Author-X-Name-Last: Larocque Author-Name: Riina Haataja Author-X-Name-First: Riina Author-X-Name-Last: Haataja Author-Name: Jaakko Nevalainen Author-X-Name-First: Jaakko Author-X-Name-Last: Nevalainen Author-Name: Hannu Oja Author-X-Name-First: Hannu Author-X-Name-Last: Oja Title: Two sample tests for the nonparametric Behrens–Fisher problem with clustered data Abstract: In this paper, we consider the nonparametric Behrens–Fisher problem with cluster-correlated data. A class of weighted Mann–Whitney test statistics is introduced and studied. In particular, a comparison with other recent testing procedures for related problems is provided. The new tests are valid when the distributions do not have the same scales and/or shapes under the null hypothesis. A general class of weighted U-statistics for clustered data, encompassing the Mann–Whitney statistic, is also introduced. A simulation studies the type I error robustness and the power of the new and of some recently proposed procedures. This study shows that the incorporation of appropriate weights can greatly improve the power of the test. A real data example illustrates the use of the tests. Journal: Journal of Nonparametric Statistics Pages: 755-771 Issue: 6 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903469728 File-URL: http://hdl.handle.net/10.1080/10485250903469728 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:6:p:755-771 Template-Type: ReDIF-Article 1.0 Author-Name: Ana Bianco Author-X-Name-First: Ana Author-X-Name-Last: Bianco Author-Name: Graciela Boente Author-X-Name-First: Graciela Author-X-Name-Last: Boente Title: On a partly linear autoregressive model with moving average errors Abstract: In this paper, we generalise the partly linear autoregression model considered in the literature by including moving average errors when we want to allow a large dependence to the past observations. The strong ergodicity of the process is derived. A consistent procedure to estimate the parametric and nonparametric components is provided together with a test statistic that allows to check the presence of a moving average component in the model. Also, a Monte Carlo study is carried out to check the performance of the given proposals. Journal: Journal of Nonparametric Statistics Pages: 797-820 Issue: 6 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903469744 File-URL: http://hdl.handle.net/10.1080/10485250903469744 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:6:p:797-820 Template-Type: ReDIF-Article 1.0 Author-Name: Evarist Giné Author-X-Name-First: Evarist Author-X-Name-Last: Giné Author-Name: Hailin Sang Author-X-Name-First: Hailin Author-X-Name-Last: Sang Title: Uniform asymptotics for kernel density estimators with variable bandwidths Abstract: It is shown that the Hall, Hu and Marron [Hall, P., Hu, T., and Marron J.S. (1995), ‘Improved Variable Window Kernel Estimates of Probability Densities’, Annals of Statistics, 23, 1–10] modification of Abramson's [Abramson, I. (1982), ‘On Bandwidth Variation in Kernel Estimates – A Square-root Law’, Annals of Statistics, 10, 1217–1223] variable bandwidth kernel density estimator satisfies the optimal asymptotic properties for estimating densities with four uniformly continuous derivatives, uniformly on bounded sets where the preliminary estimator of the density is bounded away from zero. Journal: Journal of Nonparametric Statistics Pages: 773-795 Issue: 6 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903483331 File-URL: http://hdl.handle.net/10.1080/10485250903483331 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:6:p:773-795 Template-Type: ReDIF-Article 1.0 Author-Name: J. A. Ferreira Author-X-Name-First: J. A. Author-X-Name-Last: Ferreira Title: Confidence intervals for the treatment effect on the treated Abstract: The average effect of the treatment on the treated is a quantity of interest in observational studies in which no definite parameter can be used to quantify the treatment effect, such as those where only a random subset of the data obtained by stratification can be used for analysis. Nonparametric confidence intervals for this quantity appear to be known only in the case where the responses to the treatment are binary and the data fall into a single stratum. We propose nonparametric confidence intervals for the average effect of the treatment on the treated in studies involving one or more strata and general numerical responses. Journal: Journal of Nonparametric Statistics Pages: 477-490 Issue: 3 Volume: 29 Year: 2017 Month: 7 X-DOI: 10.1080/10485252.2017.1324623 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1324623 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:3:p:477-490 Template-Type: ReDIF-Article 1.0 Author-Name: Minjung Kwak Author-X-Name-First: Minjung Author-X-Name-Last: Kwak Title: Estimation and inference of the joint conditional distribution for multivariate longitudinal data using nonparametric copulas Abstract: In this paper we study estimating the joint conditional distributions of multivariate longitudinal outcomes using regression models and copulas. For the estimation of marginal models, we consider a class of time-varying transformation models and combine the two marginal models using nonparametric empirical copulas. Our models and estimation method can be applied in many situations where the conditional mean-based models are not good enough. Empirical copulas combined with time-varying transformation models may allow quite flexible modelling for the joint conditional distributions for multivariate longitudinal data. We derive the asymptotic properties for the copula-based estimators of the joint conditional distribution functions. For illustration we apply our estimation method to an epidemiological study of childhood growth and blood pressure. Journal: Journal of Nonparametric Statistics Pages: 491-514 Issue: 3 Volume: 29 Year: 2017 Month: 7 X-DOI: 10.1080/10485252.2017.1324966 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1324966 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:3:p:491-514 Template-Type: ReDIF-Article 1.0 Author-Name: Inga Samonenko Author-X-Name-First: Inga Author-X-Name-Last: Samonenko Author-Name: John Robinson Author-X-Name-First: John Author-X-Name-Last: Robinson Title: A likelihood ratio like permutation test for one way designs Abstract: We consider permutation tests based on a likelihood ratio like statistic for the one way or k sample design used in an example in Kolassa and Robinson [(2011), ‘Saddlepoint Approximations for Likelihood Ratio Like Statistics with Applications to Permutation Tests’, Annals of Statistics, 39, 3357–3368]. We give explicitly the region in which the statistic exists, obtaining results which permit calculation of the statistic on the boundary of this region. Numerical examples are given to illustrate improvement in the power of the tests compared to the classical statistics for long-tailed error distributions and no loss of power for normal error distributions. Journal: Journal of Nonparametric Statistics Pages: 515-530 Issue: 3 Volume: 29 Year: 2017 Month: 7 X-DOI: 10.1080/10485252.2017.1324967 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1324967 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:3:p:515-530 Template-Type: ReDIF-Article 1.0 Author-Name: N. Balakrishna Author-X-Name-First: N. Author-X-Name-Last: Balakrishna Author-Name: Hira L. Koul Author-X-Name-First: Hira L. Author-X-Name-Last: Koul Title: Varying kernel marginal density estimator for a positive time series Abstract: This paper analyses the large sample behaviour of a varying kernel density estimator of the marginal density of a non-negative stationary and ergodic time series that is also strongly mixing. In particular we obtain an approximation for bias, mean square error and establish asymptotic normality of this density estimator. We also derive an almost sure uniform consistency rate over bounded intervals of this estimator. A finite sample simulation shows some superiority of the proposed density estimator over the one based on a symmetric kernel. Journal: Journal of Nonparametric Statistics Pages: 531-552 Issue: 3 Volume: 29 Year: 2017 Month: 7 X-DOI: 10.1080/10485252.2017.1324968 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1324968 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:3:p:531-552 Template-Type: ReDIF-Article 1.0 Author-Name: Marissa D. Eckrote Author-X-Name-First: Marissa D. Author-X-Name-Last: Eckrote Author-Name: Melissa A. Bingham Author-X-Name-First: Melissa A. Author-X-Name-Last: Bingham Title: A permutation test for the spread of three-dimensional rotation data Abstract: The permutation test is a nonparametric test that can be used to compare measures of spread for two data sets, but is yet to be explored in the context of three-dimensional rotation data. A permutation test for such data is developed and the statistical power of this test is considered under various conditions. The test is then used in a brief application comparing movement around the calcaneocuboid joint for a human, chimpanzee, and baboon. Journal: Journal of Nonparametric Statistics Pages: 553-560 Issue: 3 Volume: 29 Year: 2017 Month: 7 X-DOI: 10.1080/10485252.2017.1339304 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1339304 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:3:p:553-560 Template-Type: ReDIF-Article 1.0 Author-Name: Zengyan Fan Author-X-Name-First: Zengyan Author-X-Name-Last: Fan Author-Name: Heng Lian Author-X-Name-First: Heng Author-X-Name-Last: Lian Title: Interquantile shrinkage in additive models Abstract: In this paper, we investigate the commonality of nonparametric component functions among different quantile levels in additive regression models. We propose two fused adaptive group Least Absolute Shrinkage and Selection Operator penalties to shrink the difference of functions between neighbouring quantile levels. The proposed methodology is able to simultaneously estimate the nonparametric functions and identify the quantile regions where functions are unvarying, and thus is expected to perform better than standard additive quantile regression when there exists a region of quantile levels on which the functions are unvarying. Under some regularity conditions, the proposed penalised estimators can theoretically achieve the optimal rate of convergence and identify the true varying/unvarying regions consistently. Simulation studies and a real data application show that the proposed methods yield good numerical results. Journal: Journal of Nonparametric Statistics Pages: 561-576 Issue: 3 Volume: 29 Year: 2017 Month: 7 X-DOI: 10.1080/10485252.2017.1339305 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1339305 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:3:p:561-576 Template-Type: ReDIF-Article 1.0 Author-Name: Jiwei Zhao Author-X-Name-First: Jiwei Author-X-Name-Last: Zhao Title: Reducing bias for maximum approximate conditional likelihood estimator with general missing data mechanism Abstract: In missing data analysis, the assumption of the missing data mechanism is crucial. Under different assumptions, different statistical methods have to be developed accordingly; however, in reality this kind of assumption is usually unverifiable. Therefore a less stringent, and hence more flexible, assumption is preferred. In this paper, we consider a generally applicable missing data mechanism. Under this general missing data mechanism, we introduce the conditional likelihood and its approximate version as the base for estimating the unknown parameter of interest. Since this approximate conditional likelihood uses the completely observed samples only, it may result in large estimation bias, which could deteriorate the statistical inference and also jeopardise other statistical procedure. To tackle this problem, we propose to use some resampling techniques to reduce the estimation bias. We consider both the Jackknife and the Bootstrap in our paper. We compare their asymptotic biases through a higher order expansion up to $ O(n^{-1}) $ O(n−1). We also derive some results for the mean squared error (MSE) in terms of estimation accuracy. We conduct comprehensive simulation studies under different situations to illustrate our proposed method. We also apply our method to a prostate cancer data analysis. Journal: Journal of Nonparametric Statistics Pages: 577-593 Issue: 3 Volume: 29 Year: 2017 Month: 7 X-DOI: 10.1080/10485252.2017.1339306 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1339306 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:3:p:577-593 Template-Type: ReDIF-Article 1.0 Author-Name: Lei Wang Author-X-Name-First: Lei Author-X-Name-Last: Wang Author-Name: Guangming Deng Author-X-Name-First: Guangming Author-X-Name-Last: Deng Title: Dimension-reduced empirical likelihood inference for response mean with data missing at random Abstract: To make efficient inference for mean of a response variable when the data are missing at random and the dimension of covariate is not low, we construct three bias-corrected empirical likelihood (EL) methods in conjunction with dimension-reduced kernel estimation of propensity or/and conditional mean response function. Consistency and asymptotic normality of the maximum dimension-reduced EL estimators are established. We further study the asymptotic properties of the resulting dimension-reduced EL ratio functions and the corresponding EL confidence intervals for the response mean are constructed. The finite-sample performance of the proposed estimators is studied through simulation, and an application to HIV-CD4 data set is also presented. Journal: Journal of Nonparametric Statistics Pages: 594-614 Issue: 3 Volume: 29 Year: 2017 Month: 7 X-DOI: 10.1080/10485252.2017.1339307 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1339307 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:3:p:594-614 Template-Type: ReDIF-Article 1.0 Author-Name: Lei Liu Author-X-Name-First: Lei Author-X-Name-Last: Liu Author-Name: Zhihua Sun Author-X-Name-First: Zhihua Author-X-Name-Last: Sun Title: Kernel-based global MLE of partial linear random effects models for longitudinal data Abstract: Random effects models have been playing a critical role for modelling longitudinal data. However, there are little studies on the kernel-based maximum likelihood method for semiparametric random effects models. In this paper, based on kernel and likelihood methods, we propose a pooled global maximum likelihood method for the partial linear random effects models. The pooled global maximum likelihood method employs the local approximations of the nonparametric function at a group of grid points simultaneously, instead of one point. Gaussian quadrature is used to approximate the integration of likelihood with respect to random effects. The asymptotic properties of the proposed estimators are rigorously studied. Simulation studies are conducted to demonstrate the performance of the proposed approach. We also apply the proposed method to analyse correlated medical costs in the Medical Expenditure Panel Survey data set. Journal: Journal of Nonparametric Statistics Pages: 615-635 Issue: 3 Volume: 29 Year: 2017 Month: 7 X-DOI: 10.1080/10485252.2017.1339308 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1339308 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:3:p:615-635 Template-Type: ReDIF-Article 1.0 Author-Name: M. I. Borrajo Author-X-Name-First: M. I. Author-X-Name-Last: Borrajo Author-Name: W. González-Manteiga Author-X-Name-First: W. Author-X-Name-Last: González-Manteiga Author-Name: M. D. Martínez-Miranda Author-X-Name-First: M. D. Author-X-Name-Last: Martínez-Miranda Title: Bandwidth selection for kernel density estimation with length-biased data Abstract: Length-biased data are a particular case of weighted data, which arise in many situations: biomedicine, quality control or epidemiology among others. In this paper we study the theoretical properties of kernel density estimation in the context of length-biased data, proposing two consistent bootstrap methods that we use for bandwidth selection. Apart from the bootstrap bandwidth selectors we suggest a rule-of-thumb. These bandwidth selection proposals are compared with a least-squares cross-validation method. A simulation study is accomplished to understand the behaviour of the procedures in finite samples. Journal: Journal of Nonparametric Statistics Pages: 636-668 Issue: 3 Volume: 29 Year: 2017 Month: 7 X-DOI: 10.1080/10485252.2017.1339309 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1339309 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:3:p:636-668 Template-Type: ReDIF-Article 1.0 Author-Name: Hairui Hua Author-X-Name-First: Hairui Author-X-Name-Last: Hua Author-Name: Prakash N. Patil Author-X-Name-First: Prakash N. Author-X-Name-Last: Patil Author-Name: Dimitrios Bagkavos Author-X-Name-First: Dimitrios Author-X-Name-Last: Bagkavos Title: Semiparametric smoothing approach to hazard rate estimation Abstract: This research extends the multiplicative density estimation technique of Naito [(2004), ‘Semiparametric Density Estimation by Local $ L_2 $ L2-fitting’, The Annals of Statistics, 32, 1162–1191] to the hazard rate setting. The proposed estimate consists of a parametric estimate of the underlying model times a nonparametric correction factor. The reasoning of this approach is first illustrated by varying the shape parameter involved in the approximation and displaying the benefits of the resulting estimate in an $ L_2 $ L2 sense for specific example distributions. The sample analogue of this approach is then used as the basis for building an estimator of the true hazard rate function. Establishing its asymptotic properties and specifically its mean square error, reveals that the suggested estimate performs better than its nonparametric counterpart. Detailed instructions are given for calculating the operational characteristics of the estimate, that is, its shape parameter and bandwidth. Finally, its practical performance is illustrated for simulated as well as a real world data example. Journal: Journal of Nonparametric Statistics Pages: 669-693 Issue: 3 Volume: 29 Year: 2017 Month: 7 X-DOI: 10.1080/10485252.2017.1344665 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1344665 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:3:p:669-693 Template-Type: ReDIF-Article 1.0 Author-Name: Wentao Gu Author-X-Name-First: Wentao Author-X-Name-Last: Gu Author-Name: Lanh Tran Author-X-Name-First: Lanh Author-X-Name-Last: Tran Title: Fixed design regression for negatively associated random fields Abstract: Data collected on the surface of the earth at different sites often have two- or three-dimensional coordinates associated with it. We assume a simple setting where these sites are integer lattice points, say, 𝒵N, N ≥ 1, in the N-dimensional Euclidean space RN. Denote n = (n1, …, nN)∈𝒵N and In = {i: i∈𝒵N, 1 ≤ ik≤nk, k = 1, …, N}. Consider a simple regression model where the design points xni's and the responses Yni's are related as follows: Yni = g(xni)+ϵni, i∈In, where xni's are fixed design points taking values in a compact subset of Rd and where g is a bounded real-valued function defined on Rd and ϵni are negatively associated random disturbances with zero means and finite variances. The function g(x) is estimated by a general linear smoother gn(x). The asymptotic normality of the estimate gn(x) is established under weak conditions, and general conditions under which the bias gn(x) tends to zero are also determined. Journal: Journal of Nonparametric Statistics Pages: 345-363 Issue: 3 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802280218 File-URL: http://hdl.handle.net/10.1080/10485250802280218 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:3:p:345-363 Template-Type: ReDIF-Article 1.0 Author-Name: TaChen Liang Author-X-Name-First: TaChen Author-X-Name-Last: Liang Title: Empirical Bayes estimation of coefficient of variation in shifted exponential distributions Abstract: We study the empirical Bayes estimation for the coefficient of variation γ=θ/(θ+μ) in a shifted exponential distribution having density p(x|θ, μ)=θ−1e −(x−μ)/θ I(x>μ), μ>0, and the parameter θ is in some finite interval [a1, a2], where 0<a1<a2<∞ are known constants. An empirical Bayes estimator ϕ˜n is constructed and its associated asymptotic optimality investigated. It is shown that the regret of ˜ ϕn converges to zero at a rate O((ln n)4/n). Journal: Journal of Nonparametric Statistics Pages: 365-378 Issue: 3 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802587992 File-URL: http://hdl.handle.net/10.1080/10485250802587992 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:3:p:365-378 Template-Type: ReDIF-Article 1.0 Author-Name: Babak Shahbaba Author-X-Name-First: Babak Author-X-Name-Last: Shahbaba Author-Name: Andrew Gentles Author-X-Name-First: Andrew Author-X-Name-Last: Gentles Author-Name: Joseph Beyene Author-X-Name-First: Joseph Author-X-Name-Last: Beyene Author-Name: Sylvia Plevritis Author-X-Name-First: Sylvia Author-X-Name-Last: Plevritis Author-Name: Celia Greenwood Author-X-Name-First: Celia Author-X-Name-Last: Greenwood Title: A Bayesian nonparametric method for model evaluation: application to genetic studies Abstract: Statistical models applied to genetic studies commonly assume linear relationships (between disease and risk factors) and simple distributional forms (by relying on asymptotic methods) for inference. However, when the sample size is small, inference using traditional asymptotic models can be problematic. Moreover, the gene-disease relationship is not always linear. In this article, we present a new nonparametric Bayesian method for model assessment, and we demonstrate the advantages of this approach particularly when the sample size is small and/or the true model is non-linear. We evaluate our approach on simulated data and find that it performs substantially better than alternative models. We also apply our method to two real studies: diagnosis of conventional high-grade non-metastatic osteosarcoma, and survival in Burkitt's lymphoma. Journal: Journal of Nonparametric Statistics Pages: 379-396 Issue: 3 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802613558 File-URL: http://hdl.handle.net/10.1080/10485250802613558 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:3:p:379-396 Template-Type: ReDIF-Article 1.0 Author-Name: Qing Kang Author-X-Name-First: Qing Author-X-Name-Last: Kang Author-Name: Paul Nelson Author-X-Name-First: Paul Author-X-Name-Last: Nelson Title: Permutation tests from biased samples for the equality of two distributions Abstract: Suppose that independent samples are taken from two distributions according to two biased (nonrandom) sampling plans. This study constructs a class of biased-adjusted permutation tests for the equality of the two distributions. A resampling algorithm that generates permutations with unequal probabilities is proposed to estimate the tests’ exact P-values with a manageable Monte Carlo simulation error. This algorithm leads to the derivation of large-sample, normal theory tests. Conditions under which these tests are consistent are given. The tests’ power at finite sample sizes is examined via a simulation study. Journal: Journal of Nonparametric Statistics Pages: 305-319 Issue: 3 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802617617 File-URL: http://hdl.handle.net/10.1080/10485250802617617 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:3:p:305-319 Template-Type: ReDIF-Article 1.0 Author-Name: Jichang Du Author-X-Name-First: Jichang Author-X-Name-Last: Du Author-Name: Anton Schick Author-X-Name-First: Anton Author-X-Name-Last: Schick Title: A covariate-matched estimator of the error variance in nonparametric regression Abstract: There are two classes of estimators for the error variance in nonparametric regression: residual-based estimators and difference-based estimators. Residual-based estimators require an estimator of the regression function and are asymptotically equivalent to the sample variance based on the actual errors. Difference-based estimators avoid estimating the regression function and are thus simpler to calculate. They also possess superior bias properties at the expense of larger variances. Müller et al. [U.U. Müller, A. Schick, and W. Wefelmeyer, Estimating the error variance in nonparametric regression by a covariate-matched U-statistics, Statistics 37 (2003), pp. 179–188.] suggested improving difference-based estimators using covariate matching. They showed that a covariate-matched version of Rice's [J. Rice, Bandwidth choice for nonparametric regression, Ann. Statist. 12 (1984), pp. 1215–1230.] difference-based estimator matches the asymptotic performance of residual-based estimators, yet still possesses the good bias properties of Rice's estimator. Here we prove a similar result for a covariate-matched version of the difference-based estimator of Gasser et al. [T. Gasser, L. Sroka, and C. Jennen-Steinmetz, Residual variance and residual pattern in nonlinear regression, Biometrika 73 (1986), pp. 625–633.] as their estimator has even better bias properties than Rice's estimator. Journal: Journal of Nonparametric Statistics Pages: 263-285 Issue: 3 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802626873 File-URL: http://hdl.handle.net/10.1080/10485250802626873 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:3:p:263-285 Template-Type: ReDIF-Article 1.0 Author-Name: Monica Pratesi Author-X-Name-First: Monica Author-X-Name-Last: Pratesi Author-Name: M. Ranalli Author-X-Name-First: M. Author-X-Name-Last: Ranalli Author-Name: Nicola Salvati Author-X-Name-First: Nicola Author-X-Name-Last: Salvati Title: Nonparametric -quantile regression using penalised splines Abstract: Quantile regression investigates the conditional quantile functions of a response variable in terms of a set of covariates. M-quantile regression extends this idea by a ‘quantile-like’ generalisation of regression based on influence functions. In this work, we extend it to nonparametric regression, in the sense that the M-quantile regression functions do not have to be assumed to have a certain parametric form, but can be left undefined and estimated from the data. Penalised splines are employed to estimate them. This choice makes it easy to move to bivariate smoothing and semiparametric modelling. An algorithm based on iteratively reweighted penalised least squares to actually fit the model is proposed. Quantile crossing is addressed using an a posteriori adjustment to the function fits following He [1]. Simulation studies show the finite sample properties of the proposed estimation technique. Journal: Journal of Nonparametric Statistics Pages: 287-304 Issue: 3 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802638290 File-URL: http://hdl.handle.net/10.1080/10485250802638290 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:3:p:287-304 Template-Type: ReDIF-Article 1.0 Author-Name: Shota Gugushvili Author-X-Name-First: Shota Author-X-Name-Last: Gugushvili Title: Nonparametric estimation of the characteristic triplet of a discretely observed Lévy process Abstract: Given a discrete time sample X1, … Xn from a Lévy process X=(Xt)t≥0 of a finite jump activity, we study the problem of nonparametric estimation of the characteristic triplet (γ, σ2, ρ) corresponding to the process X. Based on Fourier inversion and kernel smoothing, we propose estimators of γ, σ2 and ρ and study their asymptotic behaviour. The obtained results include derivation of upper bounds on the mean square error of the estimators of γ and σ2 and an upper bound on the mean integrated square error of an estimator of ρ. Journal: Journal of Nonparametric Statistics Pages: 321-343 Issue: 3 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802645824 File-URL: http://hdl.handle.net/10.1080/10485250802645824 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:3:p:321-343 Template-Type: ReDIF-Article 1.0 Author-Name: Guoxiang Liu Author-X-Name-First: Guoxiang Author-X-Name-Last: Liu Author-Name: Xiuli Du Author-X-Name-First: Xiuli Author-X-Name-Last: Du Author-Name: Mengmeng Wang Author-X-Name-First: Mengmeng Author-X-Name-Last: Wang Author-Name: Jinguan Lin Author-X-Name-First: Jinguan Author-X-Name-Last: Lin Author-Name: Qibing Gao Author-X-Name-First: Qibing Author-X-Name-Last: Gao Title: Semiparametric jump-preserving estimation for single-index models Abstract: Estimation of the single-index model with a discontinuous unknown link function is considered in this paper. Existed refined minimum average variance estimation (rMAVE) method can estimate the single-index parameter and unknown link function simultaneously by minimising the average pointwise conditional variance, where the conditional variance can be estimated using the local linear fit method with centred kernel function. When there are jumps in the link function, big biases around jumps can appear. For this reason, we embed the jump-preserving technique in the rMAVE method, then propose an adaptive jump-preserving estimation procedure for the single-index model. Concretely speaking, the conditional variance is obtained by the one among local linear fits with centred, left-sided and right-sided kernel functions who has minimum weighted residual mean squares. The resulting estimators can preserve the jumps well and also give smooth estimates of the continuity parts. Asymptotic properties are established under some mild conditions. Simulations and real data analysis show the proposed method works well. Journal: Journal of Nonparametric Statistics Pages: 556-580 Issue: 3 Volume: 30 Year: 2018 Month: 7 X-DOI: 10.1080/10485252.2018.1444164 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1444164 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:3:p:556-580 Template-Type: ReDIF-Article 1.0 Author-Name: Huapeng Li Author-X-Name-First: Huapeng Author-X-Name-Last: Li Author-Name: Yang Liu Author-X-Name-First: Yang Author-X-Name-Last: Liu Author-Name: Yukun Liu Author-X-Name-First: Yukun Author-X-Name-Last: Liu Author-Name: Riquan Zhang Author-X-Name-First: Riquan Author-X-Name-Last: Zhang Title: Comparison of empirical likelihood and its dual likelihood under density ratio model Abstract: Density ratio models (DRMs) are commonly used semiparametric models to link related populations. Empirical likelihood (EL) under DRM has been demonstrated to be a flexible and useful platform for semiparametric inferences. Since DRM-based EL has the same maximum point and maximum likelihood as its dual form (dual EL), EL-based inferences under DRM are usually made through the latter. A natural question comes up: is there any efficiency loss of doing so? We make a careful comparison of the dual EL and DRM-based EL estimation methods from theory and numerical simulations. We find that their point estimators for any parameter are exactly the same, while they may have different performances in interval estimation. In terms of coverage accuracy, the two intervals are comparable for non- or moderate skewed populations, and the DRM-based EL interval can be much superior for severely skewed populations. A real data example is analysed for illustration purpose. Journal: Journal of Nonparametric Statistics Pages: 581-597 Issue: 3 Volume: 30 Year: 2018 Month: 7 X-DOI: 10.1080/10485252.2018.1457790 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1457790 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:3:p:581-597 Template-Type: ReDIF-Article 1.0 Author-Name: Gaku Igarashi Author-X-Name-First: Gaku Author-X-Name-Last: Igarashi Author-Name: Yoshihide Kakizawa Author-X-Name-First: Yoshihide Author-X-Name-Last: Kakizawa Title: Generalised gamma kernel density estimation for nonnegative data and its bias reduction Abstract: We consider density estimation for nonnegative data using generalised gamma density. What is being emphasised here is that a negative exponent is allowed. We show that, for each positive or negative exponent, (i) generalised gamma kernel density estimator, without bias reduction, has the mean integrated squared error (MISE) of order $ O(n^{-4/5}) $ O(n−4/5), as in other boundary-bias-free density estimators from the existing literature, and that (ii) the bias-reduced versions have the MISEs of order $ O(n^{-8/9}) $ O(n−8/9), where n is the sample size. We illustrate the finite sample performance of the proposed estimators through the simulations. Journal: Journal of Nonparametric Statistics Pages: 598-639 Issue: 3 Volume: 30 Year: 2018 Month: 7 X-DOI: 10.1080/10485252.2018.1457791 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1457791 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:3:p:598-639 Template-Type: ReDIF-Article 1.0 Author-Name: Huadong Zhao Author-X-Name-First: Huadong Author-X-Name-Last: Zhao Author-Name: Wanzhu Tu Author-X-Name-First: Wanzhu Author-X-Name-Last: Tu Author-Name: Zhangsheng Yu Author-X-Name-First: Zhangsheng Author-X-Name-Last: Yu Title: A nonparametric time-varying coefficient model for panel count data Abstract: In this research, we describe a nonparametric time-varying coefficient model for the analysis of panel count data. We extend the traditional panel count data models by incorporating B-splines estimates of time-varying coefficients. We show that the proposed model can be implemented using a nonparametric maximum pseudo-likelihood method. We further examine the theoretical properties of the estimators of model parameters. The operational characteristics of the proposed method are evaluated through a simulation study. For illustration, we analyse data from a study of childhood wheezing, and describe the time-varying effect of an inflammatory marker on the risk of wheezing. Journal: Journal of Nonparametric Statistics Pages: 640-661 Issue: 3 Volume: 30 Year: 2018 Month: 7 X-DOI: 10.1080/10485252.2018.1458982 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1458982 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:3:p:640-661 Template-Type: ReDIF-Article 1.0 Author-Name: Lei Wang Author-X-Name-First: Lei Author-X-Name-Last: Wang Author-Name: Dan Yang Author-X-Name-First: Dan Author-X-Name-Last: Yang Title: F-distribution calibrated empirical likelihood ratio tests for multiple hypothesis testing Abstract: Multiple hypothesis testing can be important tools when conclusions are drawn by simultaneous testing of a large number of hypotheses in bioinformatics, general medicine, pharmacology and epidemiology. In this paper, we consider three nonparametric empirical likelihood ratio tests (ELRTs) for multiple hypothesis testing problems. When the number of hypotheses is far larger than sample size, however, these ELRTs using asymptotic chi-square calibration generally have much higher false discovery rate (FDR) and can be quite anti-conservative. We find that the first order term of the empirical likelihood ratio statistic closely resembles Hotelling's $T^2$T2 statistic admitting limiting F distributions for small sample size. Motivated by this result, we propose the F-distribution calibrated ELRTs. Simulation results indicate that the proposed tests not only can control the FDR in the acceptable range, but also guarantee the test efficacy in terms of maximising the number of discoveries for small and moderate sample sizes. Two real data applications are also included for illustration. Journal: Journal of Nonparametric Statistics Pages: 662-679 Issue: 3 Volume: 30 Year: 2018 Month: 7 X-DOI: 10.1080/10485252.2018.1461867 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1461867 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:3:p:662-679 Template-Type: ReDIF-Article 1.0 Author-Name: Seonjin Kim Author-X-Name-First: Seonjin Author-X-Name-Last: Kim Author-Name: Zhibiao Zhao Author-X-Name-First: Zhibiao Author-X-Name-Last: Zhao Author-Name: Zhijie Xiao Author-X-Name-First: Zhijie Author-X-Name-Last: Xiao Title: Efficient estimation for time-varying coefficient longitudinal models Abstract: For estimation of time-varying coefficient longitudinal models, the widely used local least-squares (LS) or covariance-weighted local LS smoothing uses information from the local sample average. Motivated by the fact that a combination of multiple quantiles provides a more complete picture of the distribution, we investigate quantile regression-based methods to improve efficiency by optimally combining information across quantiles. Under the working independence scenario, the asymptotic variance of the proposed estimator approaches the Cramér–Rao lower bound. In the presence of dependence among within-subject measurements, we adopt a prewhitening technique to transform regression errors into independent innovations and show that the prewhitened optimally weighted quantile average estimator asymptotically achieves the Cramér–Rao bound for the independent innovations. Fully data-driven bandwidth selection and optimal weights estimation are implemented through a two-step procedure. Monte Carlo studies show that the proposed method delivers more robust and superior overall performance than that of the existing methods. Journal: Journal of Nonparametric Statistics Pages: 680-702 Issue: 3 Volume: 30 Year: 2018 Month: 7 X-DOI: 10.1080/10485252.2018.1467415 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1467415 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:3:p:680-702 Template-Type: ReDIF-Article 1.0 Author-Name: Hui Zhao Author-X-Name-First: Hui Author-X-Name-Last: Zhao Author-Name: Chenchen Ma Author-X-Name-First: Chenchen Author-X-Name-Last: Ma Author-Name: Junlong Li Author-X-Name-First: Junlong Author-X-Name-Last: Li Author-Name: Jianguo Sun Author-X-Name-First: Jianguo Author-X-Name-Last: Sun Title: Regression analysis of clustered interval-censored failure time data with linear transformation models in the presence of informative cluster size Abstract: This paper discusses regression analysis of clustered interval-censored failure time data, which often occur in medical follow-up studies among other areas. For such data, sometimes the failure time may be related to the cluster size, the number of subjects within each cluster or we have informative cluster sizes. For the problem, we present a within-cluster resampling method for the situation where the failure time of interest can be described by a class of linear transformation models. In addition to the establishment of the asymptotic properties of the proposed estimators of regression parameters, an extensive simulation study is conducted for the assessment of the finite sample properties of the proposed method and suggests that it works well in practical situations. An application to the example that motivated this study is also provided. Journal: Journal of Nonparametric Statistics Pages: 703-715 Issue: 3 Volume: 30 Year: 2018 Month: 7 X-DOI: 10.1080/10485252.2018.1469755 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1469755 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:3:p:703-715 Template-Type: ReDIF-Article 1.0 Author-Name: Taihe Yi Author-X-Name-First: Taihe Author-X-Name-Last: Yi Author-Name: Zhengming Wang Author-X-Name-First: Zhengming Author-X-Name-Last: Wang Author-Name: Dongyun Yi Author-X-Name-First: Dongyun Author-X-Name-Last: Yi Title: Bayesian sieve methods: approximation rates and adaptive posterior contraction rates Abstract: In the last 20 years, a lot of achievements have been made in the study of posterior contraction rates of nonparametric Bayesian methods, and plenty of them involve sieve priors, but mainly for specific models or sieves. We provide a posterior contraction theorem for general parametric sieve priors. The theorem has weaker and simpler conditions compared with the existing results, and indicates that the sieve prior is rate adaptive. We apply the general theorem to density estimations and nonparametric regression with jumps. We also provided a reversible jump MCMC (Markov Chain Monte Carlo) algorithm for the sieve prior. Journal: Journal of Nonparametric Statistics Pages: 716-741 Issue: 3 Volume: 30 Year: 2018 Month: 7 X-DOI: 10.1080/10485252.2018.1470241 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1470241 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:3:p:716-741 Template-Type: ReDIF-Article 1.0 Author-Name: Christian Palmes Author-X-Name-First: Christian Author-X-Name-Last: Palmes Author-Name: Benedikt Funke Author-X-Name-First: Benedikt Author-X-Name-Last: Funke Author-Name: Babak Sayyid Hosseini Author-X-Name-First: Babak Sayyid Author-X-Name-Last: Hosseini Title: Nonparametric low-frequency Lévy copula estimation in a general framework Abstract: Let X be a d-dimensional Lévy process. Given the low-frequency observations $ X_t $ Xt, $ t=1,\ldots ,n $ t=1,…,n, the dependence structure of the jumps of X is estimated. In general, the Lévy measure ν describes the average jump behaviour in a time unit. Thus the aim is to estimate the dependence structure of ν by estimating the so-called Lévy copula $ \mathfrak {C} $ C of ν. We generalise known one-dimensional low-frequency techniques to construct a Lévy copula estimator $ \hat {\mathfrak {C}}_n $ Cˆn based on the above-mentioned n observations and prove $ \hat {\mathfrak {C}}_n \to \mathfrak {C} $ Cˆn→C, $ n\to \infty $ n→∞, uniformly on compact sets bounded away from zero with the rate of convergence $ \sqrt {\log n} $ log⁡n that is optimal in a certain sense. This convergence holds under quite general assumptions which also include Lévy triplets $ (\Sigma , \nu , \alpha ) $ (Σ,ν,α) with non-vanishing Brownian part $ \Sigma \neq 0 $ Σ≠0 and ν of arbitrary Blumenthal–Getoor index $ 0\le \beta \le 2 $ 0≤β≤2. Journal: Journal of Nonparametric Statistics Pages: 523-555 Issue: 3 Volume: 30 Year: 2018 Month: 7 X-DOI: 10.1080/10485252.2018.1474215 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1474215 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:3:p:523-555 Template-Type: ReDIF-Article 1.0 Author-Name: Frederic Paik Schoenberg Author-X-Name-First: Frederic Paik Author-X-Name-Last: Schoenberg Author-Name: Joshua Seth Gordon Author-X-Name-First: Joshua Seth Author-X-Name-Last: Gordon Author-Name: Ryan J. Harrigan Author-X-Name-First: Ryan J. Author-X-Name-Last: Harrigan Title: Analytic computation of nonparametric Marsan–Lengliné estimates for Hawkes point processes Abstract: In 2008, Marsan and Lengliné presented a nonparametric way to estimate the triggering function of a Hawkes process. Their method requires an iterative and computationally intensive procedure which ultimately produces only approximate maximum likelihood estimates (MLEs) whose asymptotic properties are poorly understood. Here, we note a mathematical curiosity that allows one to compute, directly and extremely rapidly, exact MLEs of the nonparametric triggering function. The method here requires that the number q of intervals on which the nonparametric estimate is sought equals the number n of observed points. The resulting estimates have very high variance but may be smoothed to form more stable estimates. The performance and computational efficiency of the proposed method is verified in two disparate, highly challenging simulation scenarios: first to estimate the triggering functions, with simulation-based 95% confidence bands, for earthquakes and their aftershocks in Loma Prieta, California, and second, to characterise triggering in confirmed cases of plague in the United States over the last century. In both cases, the proposed estimator can be used to describe the rate of contagion of the processes in detail, and the computational efficiency of the estimator facilitates the construction of simulation-based confidence intervals. Journal: Journal of Nonparametric Statistics Pages: 742-757 Issue: 3 Volume: 30 Year: 2018 Month: 7 X-DOI: 10.1080/10485252.2018.1475663 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1475663 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:3:p:742-757 Template-Type: ReDIF-Article 1.0 Author-Name: Peijie Wang Author-X-Name-First: Peijie Author-X-Name-Last: Wang Author-Name: Hui Zhao Author-X-Name-First: Hui Author-X-Name-Last: Zhao Author-Name: Mingyue Du Author-X-Name-First: Mingyue Author-X-Name-Last: Du Author-Name: Jianguo Sun Author-X-Name-First: Jianguo Author-X-Name-Last: Sun Title: Inference on semiparametric transformation model with general interval-censored failure time data Abstract: Failure time data occur in many areas and in various censoring forms and many models have been proposed for their regression analysis such as the proportional hazards model and the proportional odds model. Another choice that has been discussed in the literature is a general class of semiparmetric transformation models, which include the two models above and many others as special cases. In this paper, we consider this class of models when one faces a general type of censored data, case K informatively interval-censored data, for which there does not seem to exist an established inference procedure. For the problem, we present a two-step estimation procedure that is quite flexible and can be easily implemented, and the consistency and asymptotic normality of the proposed estimators of regression parameters are established. In addition, an extensive simulation study is conducted and suggests that the proposed procedure works well for practical situations. An application is also provided. Journal: Journal of Nonparametric Statistics Pages: 758-773 Issue: 3 Volume: 30 Year: 2018 Month: 7 X-DOI: 10.1080/10485252.2018.1478091 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1478091 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:3:p:758-773 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Grabchak Author-X-Name-First: Michael Author-X-Name-Last: Grabchak Author-Name: Zhiyi Zhang Author-X-Name-First: Zhiyi Author-X-Name-Last: Zhang Title: Asymptotic normality for plug-in estimators of diversity indices on countable alphabets Abstract: The plug-in estimator is one of the most popular approaches to the estimation of diversity indices. In this paper, we study its asymptotic distribution for a large class of diversity indices on countable alphabets. In particular, we give conditions for the plug-in estimator to be asymptotically normal, and in the case of uniform distributions, where asymptotic normality fails, we give conditions for the asymptotic distribution to be chi-squared. Our results cover some of the most commonly used indices, including Simpson's index, Reńyi's entropy and Shannon's entropy. Journal: Journal of Nonparametric Statistics Pages: 774-795 Issue: 3 Volume: 30 Year: 2018 Month: 7 X-DOI: 10.1080/10485252.2018.1482294 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1482294 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:3:p:774-795 Template-Type: ReDIF-Article 1.0 Author-Name: Ji Chen Author-X-Name-First: Ji Author-X-Name-Last: Chen Author-Name: Fang Fang Author-X-Name-First: Fang Author-X-Name-Last: Fang Author-Name: Zhiguo Xiao Author-X-Name-First: Zhiguo Author-X-Name-Last: Xiao Title: Semiparametric inference for estimating equations with nonignorably missing covariates Abstract: We consider statistical inference of unknown parameters in estimating equations (EEs) when some covariates have nonignorably missing values, which is quite common in practice but has rarely been discussed in the literature. When an instrument, a fully observed covariate vector that helps identifying parameters under nonignorable missingness, is available, the conditional distribution of the missing covariates given other covariates can be estimated by the pseudolikelihood method of Zhao and Shao [(2015), ‘Semiparametric pseudo likelihoods in generalised linear models with nonignorable missing data’, Journal of the American Statistical Association, 110, 1577–1590)] and be used to construct unbiased EEs. These modified EEs then constitute a basis for valid inference by empirical likelihood. Our method is applicable to a wide range of EEs used in practice. It is semiparametric since no parametric model for the propensity of missing covariate data is assumed. Asymptotic properties of the proposed estimator and the empirical likelihood ratio test statistic are derived. Some simulation results and a real data analysis are presented for illustration. Journal: Journal of Nonparametric Statistics Pages: 796-812 Issue: 3 Volume: 30 Year: 2018 Month: 7 X-DOI: 10.1080/10485252.2018.1482295 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1482295 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:3:p:796-812 Template-Type: ReDIF-Article 1.0 Author-Name: Ursula Müller Author-X-Name-First: Ursula Author-X-Name-Last: Müller Author-Name: Anton Schick Author-X-Name-First: Anton Author-X-Name-Last: Schick Author-Name: Wolfgang Wefelmeyer Author-X-Name-First: Wolfgang Author-X-Name-Last: Wefelmeyer Title: Optimal plug-in estimators for multivariate distributions with conditionally independent components Abstract: The usual estimator for the expectation of a function of a random vector is the empirical estimator. Assume that some of the components of the random vector are conditionally independent given the other components. We construct a plug-in estimator for the expectation that uses this information, prove a central limit theorem for the estimator, and show that the estimator is asymptotically efficient in the sense of a nonparametric version of the convolution theorem of Hájek and Le Cam. Journal: Journal of Nonparametric Statistics Pages: 1031-1050 Issue: 4 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.569713 File-URL: http://hdl.handle.net/10.1080/10485252.2011.569713 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:1031-1050 Template-Type: ReDIF-Article 1.0 Author-Name: Pao-sheng Shen Author-X-Name-First: Pao-sheng Author-X-Name-Last: Shen Title: Proportional subdistribution hazards regression for left-truncated competing risks data Abstract: Fine and Gray [(1999), ‘A Proportional Hazards Model for the Subdistribution of a Competing Risk’, Journal of the American Statistical Association, 94, 496–509] considered a proportional subdistribution hazards model under the framework of competing risks. Using the partial likelihood principle and weighting techniques, they derived estimation and inference procedures for regression parameters under right censoring. In this article, we show that the partial likelihood approach to estimation is applicable when both right censoring and left truncation are present. We derive large sample properties of the proposed estimators and investigate their finite sample performances via simulation. Journal: Journal of Nonparametric Statistics Pages: 885-895 Issue: 4 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.571256 File-URL: http://hdl.handle.net/10.1080/10485252.2011.571256 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:885-895 Template-Type: ReDIF-Article 1.0 Author-Name: Shota Gugushvili Author-X-Name-First: Shota Author-X-Name-Last: Gugushvili Author-Name: Bert van Es Author-X-Name-First: Bert Author-X-Name-Last: van Es Author-Name: Peter Spreij Author-X-Name-First: Peter Author-X-Name-Last: Spreij Title: Deconvolution for an atomic distribution: rates of convergence Abstract: Let X1, …, Xn be i.i.d. copies of a random variable X=Y+Z, where Xi=Yi+Zi, and Yi and Zi are independent and have the same distribution as Y and Z, respectively. Assume that the random variables Yi’s are unobservable and that Y=AV, where A and V are independent, A has a Bernoulli distribution with probability of success equal to 1−p and V has a distribution function F with density f. Let the random variable Z have a known distribution with density k. Based on a sample X1, …, Xn, we consider the problem of nonparametric estimation of the density f and the probability p. Our estimators of f and p are constructed via Fourier inversion and kernel smoothing. We derive their convergence rates over suitable functional classes. By establishing in a number of cases the lower bounds for estimation of f and p we show that our estimators are rate-optimal in these cases. Journal: Journal of Nonparametric Statistics Pages: 1003-1029 Issue: 4 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.576763 File-URL: http://hdl.handle.net/10.1080/10485252.2011.576763 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:1003-1029 Template-Type: ReDIF-Article 1.0 Author-Name: Florian Ueltzhöfer Author-X-Name-First: Florian Author-X-Name-Last: Ueltzhöfer Author-Name: Claudia Klüppelberg Author-X-Name-First: Claudia Author-X-Name-Last: Klüppelberg Title: An oracle inequality for penalised projection estimation of Lévy densities from high-frequency observations Abstract: We consider a multivariate Lévy process given by the sum of a Brownian motion with drift and an independent time-homogeneous pure jump process governed by a Lévy density. We assume that observation of a sample path takes place on an equidistant discrete time grid. Following Grenander's method of sieves, we construct families of nonparametric projection estimators for the restriction of a Lévy density to bounded sets away from the origin. Moreover, we introduce a data-driven penalisation criterion to select an estimator within a given family, where we measure the estimation error in an L2-norm. Furthermore, we give sufficient conditions on the penalty such that an oracle inequality holds. As an application, we prove adaptiveness for sufficiently smooth Lévy densities in some Sobolev space and explicitly derive the rate of convergence. Journal: Journal of Nonparametric Statistics Pages: 967-989 Issue: 4 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.581375 File-URL: http://hdl.handle.net/10.1080/10485252.2011.581375 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:967-989 Template-Type: ReDIF-Article 1.0 Author-Name: T. Senga Kiessé Author-X-Name-First: T. Author-X-Name-Last: Senga Kiessé Author-Name: M. Rivoire Author-X-Name-First: M. Author-X-Name-Last: Rivoire Title: Discrete semiparametric regression models with associated kernel and applications Abstract: This work is concerned with a semiparametric associated kernel estimator for count explanatory variables. The proposed semiparametric estimator is a multiplicative combination between a parametric model and a discrete nonparametric kernel estimator of Nadaraya–Watson type. In this semiparametric approach, the parametric model plays the role of the start function and the nonparametric kernel estimator is a correction factor of the parametric estimate. Some asymptotic properties of the discrete semiparametric kernel regression estimator are pointed out; in particular, we show its asymptotic normality and the order of the optimal bandwidth. The parametric part is illustrated by some nonlinear and generalised linear models; for the nonparametric estimator, we apply the discrete general triangular associated kernel providing bias reduction. The usefulness of the discrete semiparametric kernel regression estimator is shown on three practical examples in comparison with logistic, generalised linear and additive models. Journal: Journal of Nonparametric Statistics Pages: 927-941 Issue: 4 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.583986 File-URL: http://hdl.handle.net/10.1080/10485252.2011.583986 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:927-941 Template-Type: ReDIF-Article 1.0 Author-Name: Christopher Withers Author-X-Name-First: Christopher Author-X-Name-Last: Withers Author-Name: Saralees Nadarajah Author-X-Name-First: Saralees Author-X-Name-Last: Nadarajah Title: Nonparametric confidence intervals for the integral of a function of an unknown density Abstract: Given a random sample of size n from an unknown distribution function F on ℝ with finite derivatives and density f, we wish to estimate for a smooth function L. Examples are t f2, the differential entropy and the Kullback–Leibler distance. We estimate f using a kernel estimate [fcirc] based on a kernel of order p, say. We show that {[fcirc](xi), i=1, …, s} satisfies the Cornish–Fisher assumption with respect to m=nh. It follows that the corresponding estimate θˆ has a bias of magnitude O(hq+m−1), where p≤q≤2p depends on L. We show that the variance of θˆ has magnitude O(n−1) for a suitable bandwidth. For the regular case, we give one-sided and two-sided confidence intervals for θ with errors of magnitude O(M−1/2) and O(M−1), where M=nh2. We present simulation studies to show the practical values of the results. Journal: Journal of Nonparametric Statistics Pages: 943-966 Issue: 4 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.576762 File-URL: http://hdl.handle.net/10.1080/10485252.2011.576762 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:943-966 Template-Type: ReDIF-Article 1.0 Author-Name: Zhenyu Liu Author-X-Name-First: Zhenyu Author-X-Name-Last: Liu Author-Name: Reza Modarres Author-X-Name-First: Reza Author-X-Name-Last: Modarres Title: Lens data depth and median Abstract: We define the lens depth (LD) function LD(t; F) of a vector t∈Rd with respect to a distribution function F to be the probability that t is contained in a random hyper-lens formed by the intersection of two closed balls centred at two i.i.d observations from F. We show that LD is a statistical depth function and explore its properties, including affine invariance, symmetry, maximality at the centre and monotonicity. We define the sample LD and investigate its uniform consistency, asymptotic normality and computational complexity in high-dimensional settings. We define the lens median (LM), a multivariate analogue of the univariate median, as the point where the LD is maximised. The sample LM is the vector that is covered by the most number of hyper-lenses formed between any two sample observations. We state its asymptotic consistency and normality and examine its breakdown point and relative efficiency. The sample LM is robust and efficient for estimating the centre of a unimodal distribution. A comparison of LD and LM to existing data depth functions and medians in terms of computational complexity, robustness, efficiency and breakdown point is presented. Journal: Journal of Nonparametric Statistics Pages: 1063-1074 Issue: 4 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.584621 File-URL: http://hdl.handle.net/10.1080/10485252.2011.584621 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:1063-1074 Template-Type: ReDIF-Article 1.0 Author-Name: Karol Dziedziul Author-X-Name-First: Karol Author-X-Name-Last: Dziedziul Author-Name: Magdalena Kucharska Author-X-Name-First: Magdalena Author-X-Name-Last: Kucharska Author-Name: Barbara Wolnik Author-X-Name-First: Barbara Author-X-Name-Last: Wolnik Title: Estimation of the smoothness of density Abstract: This paper introduces a definition where the smoothness of a function f is characterized by means of the Besov spaces , that is, there is the parameter s* such that for all s<s*, , and for all s>s*, . If f is a density with the smoothness s*, then we construct an estimator of s* which is based on histograms. Journal: Journal of Nonparametric Statistics Pages: 991-1001 Issue: 4 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.587879 File-URL: http://hdl.handle.net/10.1080/10485252.2011.587879 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:991-1001 Template-Type: ReDIF-Article 1.0 Author-Name: Wan Tang Author-X-Name-First: Wan Author-X-Name-Last: Tang Author-Name: Guoxin Zuo Author-X-Name-First: Guoxin Author-X-Name-Last: Zuo Author-Name: Hua He Author-X-Name-First: Hua Author-X-Name-Last: He Title: Double-smoothing for varying coefficient models Abstract: Moderation analyses are widely used in biomedical and psychosocial research to investigate differential treatment effects, with moderators frequently identified through testing the significance of the interaction between the predictor and the potential moderator under strong parametric assumptions. Without imposing any parametric forms on how the moderators may affect the relationship between predictors and responses, varying coefficient models address this fundamental problem of strong parametric assumptions with the current practice of moderation analysis and provide a much broader class of models for complex moderation relationships. Local polynomial, especially local linear (LL), methods are commonly used in estimating the varying coefficient models. Recently, a double-smoothing (DS) LL method has been proposed for nonparametric regression models, with nice properties compared to LL and local cubic (LC) methods. In this paper, we generalise DS to varying coefficient models, and show that it holds similar advantages over LL and LC methods. Journal: Journal of Nonparametric Statistics Pages: 917-926 Issue: 4 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.588707 File-URL: http://hdl.handle.net/10.1080/10485252.2011.588707 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:917-926 Template-Type: ReDIF-Article 1.0 Author-Name: Yoichi Nishiyama Author-X-Name-First: Yoichi Author-X-Name-Last: Nishiyama Title: Estimation for the invariant law of an ergodic diffusion process based on high-frequency data Abstract: Let a one-dimensional ergodic diffusion process X be observed at time points such that and , where , with p∈(0, 1) being a constant depending also on some conditions on X. We consider the nonparametric estimation problems for the invariant distribution and the invariant density. In both problems, we propose some estimators which are asymptotically normal and asymptotically efficient in some functional senses. Journal: Journal of Nonparametric Statistics Pages: 909-915 Issue: 4 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.591397 File-URL: http://hdl.handle.net/10.1080/10485252.2011.591397 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:909-915 Template-Type: ReDIF-Article 1.0 Author-Name: Yunlu Jiang Author-X-Name-First: Yunlu Author-X-Name-Last: Jiang Author-Name: Shaoli Wang Author-X-Name-First: Shaoli Author-X-Name-Last: Wang Author-Name: Wenxiu Ge Author-X-Name-First: Wenxiu Author-X-Name-Last: Ge Author-Name: Xueqin Wang Author-X-Name-First: Xueqin Author-X-Name-Last: Wang Title: Depth-based weighted empirical likelihood and general estimating equations Abstract: In this paper, we link the depth-based weighted empirical likelihood (WEL) with general estimating equations to produce a robust estimation of parameters for contaminated data with auxiliary information about the parameters. Such auxiliary information can be expressed through a group of functionally independent general estimating equations. Under general conditions, asymptotic properties of the WEL estimator are established. Furthermore, we prove that the WEL ratio statistic is asymptotically chi-squared distributed. Simulation studies are conducted to test the robustness of the WEL estimator. Finally, we apply the proposed method to analyse the gilgai survey data. Journal: Journal of Nonparametric Statistics Pages: 1051-1062 Issue: 4 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.594510 File-URL: http://hdl.handle.net/10.1080/10485252.2011.594510 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:1051-1062 Template-Type: ReDIF-Article 1.0 Author-Name: Néstor Aguilera Author-X-Name-First: Néstor Author-X-Name-Last: Aguilera Author-Name: Liliana Forzani Author-X-Name-First: Liliana Author-X-Name-Last: Forzani Author-Name: Pedro Morin Author-X-Name-First: Pedro Author-X-Name-Last: Morin Title: On uniform consistent estimators for convex regression Abstract: A new nonparametric estimator of a convex regression function in any dimension is proposed and its uniform convergence properties are studied. We start by using any estimator of the regression function and convexify it by taking the convex envelope of a sample of the approximation obtained. We prove that the uniform rate of convergence of the estimator is maintained after the convexification is applied. The finite-sample properties of the new estimator are investigated by means of a simulation study and the application of the new method is demonstrated in examples. Journal: Journal of Nonparametric Statistics Pages: 897-908 Issue: 4 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.597506 File-URL: http://hdl.handle.net/10.1080/10485252.2011.597506 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:897-908 Template-Type: ReDIF-Article 1.0 Author-Name: Mary Meyer Author-X-Name-First: Mary Author-X-Name-Last: Meyer Author-Name: Amber Hackstadt Author-X-Name-First: Amber Author-X-Name-Last: Hackstadt Author-Name: Jennifer Hoeting Author-X-Name-First: Jennifer Author-X-Name-Last: Hoeting Title: Bayesian estimation and inference for generalised partial linear models using shape-restricted splines Abstract: A Bayesian approach to generalised partial linear regression models is proposed, where regression functions are modelled nonparametrically using regression splines, with assumptions about shape and smoothness. The knots may be modelled as fixed or free, incorporating a reversible-jump Markov chain Monte Carlo algorithm for the latter. The modelling framework along with vague prior distributions provides more flexibility compared with other Bayesian constrained smoothers; further, the method is simpler, more intuitive, easier to implement, and computationally faster. Inference concerning parametrically modelled covariates can be accomplished using approximate marginal distributions, with standard Bayes model selection methods for more general inference. Simulations show that the inference methods have desirable Bayesian and frequentist properties. In particular, these methods often perform similarly to standard parametric methods when the parametric assumptions are met and are superior when the assumptions are violated. The R code to implement the methods described here is available at www.stat.colostate.edu/~meyer/code.htm. Journal: Journal of Nonparametric Statistics Pages: 867-884 Issue: 4 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.597852 File-URL: http://hdl.handle.net/10.1080/10485252.2011.597852 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:867-884 Template-Type: ReDIF-Article 1.0 Author-Name: Gerda Claeskens Author-X-Name-First: Gerda Author-X-Name-Last: Claeskens Author-Name: Huijuan Ding Author-X-Name-First: Huijuan Author-X-Name-Last: Ding Author-Name: Maarten Jansen Author-X-Name-First: Maarten Author-X-Name-Last: Jansen Title: Lack-of-fit tests in linear mixed models with application to wavelet tests Abstract: We obtain the asymptotic distribution of score and restricted likelihood ratio statistics for testing whether variance components are equal to zero in linear mixed models with a fixed and finite number of random effects. The main new innovation of this paper is in deriving the components of the distribution, which are not chi-squared. The proposed test statistics are used for lack-of-fit testing using wavelets, where the finest scale wavelet coefficients are allowed to have a different variance than the other wavelet coefficients in the mixed effect wavelet model. We study the power of a wavelet-based test for a hypothesised parametric model within a mixed model framework in a simulation study. Journal: Journal of Nonparametric Statistics Pages: 853-865 Issue: 4 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.598935 File-URL: http://hdl.handle.net/10.1080/10485252.2011.598935 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:853-865 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Reviewer List 1 Oct 10–30 Sep 11 Journal: Journal of Nonparametric Statistics Pages: 1075-1076 Issue: 4 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.630254 File-URL: http://hdl.handle.net/10.1080/10485252.2011.630254 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:1075-1076 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Editorial Board Journal: Journal of Nonparametric Statistics Pages: ebi-ebi Issue: 4 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.637748 File-URL: http://hdl.handle.net/10.1080/10485252.2011.637748 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:ebi-ebi Template-Type: ReDIF-Article 1.0 Author-Name: Hui-Ling Lin Author-X-Name-First: Hui-Ling Author-X-Name-Last: Lin Author-Name: Zhouping Li Author-X-Name-First: Zhouping Author-X-Name-Last: Li Author-Name: Dongliang Wang Author-X-Name-First: Dongliang Author-X-Name-Last: Wang Author-Name: Yichuan Zhao Author-X-Name-First: Yichuan Author-X-Name-Last: Zhao Title: Jackknife empirical likelihood for the error variance in linear models Abstract: Variance estimation is a fundamental yet important problem in statistical modelling. In this paper, we propose jackknife empirical likelihood (JEL) methods for the error variance in a linear regression model. We prove that the JEL ratio converges to the standard chi-squared distribution. The asymptotic chi-squared properties for the adjusted JEL and extended JEL estimators are also established. Extensive simulation studies to compare the new JEL methods with the standard method in terms of coverage probability and interval length are conducted, and the simulation results show that our proposed JEL methods perform better than the standard method. We also illustrate the proposed methods using two real data sets. Journal: Journal of Nonparametric Statistics Pages: 151-166 Issue: 2 Volume: 29 Year: 2017 Month: 4 X-DOI: 10.1080/10485252.2017.1285028 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1285028 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:151-166 Template-Type: ReDIF-Article 1.0 Author-Name: L. Baringhaus Author-X-Name-First: L. Author-X-Name-Last: Baringhaus Author-Name: N. Henze Author-X-Name-First: N. Author-X-Name-Last: Henze Title: Cramér–von Mises distance: probabilistic interpretation, confidence intervals, and neighbourhood-of-model validation Abstract: We give a probabilistic interpretation of the Cramér–von Mises distance $ \Delta (F,F_0) = \int (F-F_0)^2\,{\rm d}F_0 $ Δ(F,F0)=∫(F−F0)2dF0 between continuous distribution functions F and $ F_0 $ F0. If F is unknown, we construct an asymptotic confidence interval for $ \Delta (F,F_0) $ Δ(F,F0) based on a random sample from F. Moreover, for given $ F_0 $ F0 and some value $ \Delta _0>0 $ Δ0>0, we propose an asymptotic equivalence test of the hypothesis that $ \Delta (F,F_0) \ge \Delta _0 $ Δ(F,F0)≥Δ0 against the alternative $ \Delta (F,F_0) < \Delta _0 $ Δ(F,F0)<Δ0. If such a ‘neighbourhood-of- $ F_0 $ F0 validation test’, carried out at a small asymptotic level, rejects the hypothesis, there is evidence that F is within a distance $ \Delta _0 $ Δ0 of $ F_0 $ F0. As a neighbourhood-of-exponentiality test shows, the method may be extended to the case that $ H_0 $ H0 is composite. Journal: Journal of Nonparametric Statistics Pages: 167-188 Issue: 2 Volume: 29 Year: 2017 Month: 4 X-DOI: 10.1080/10485252.2017.1285029 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1285029 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:167-188 Template-Type: ReDIF-Article 1.0 Author-Name: Puying Zhao Author-X-Name-First: Puying Author-X-Name-Last: Zhao Author-Name: Hui Zhao Author-X-Name-First: Hui Author-X-Name-Last: Zhao Author-Name: Niansheng Tang Author-X-Name-First: Niansheng Author-X-Name-Last: Tang Author-Name: Zhaohai Li Author-X-Name-First: Zhaohai Author-X-Name-Last: Li Title: Weighted composite quantile regression analysis for nonignorable missing data using nonresponse instrument Abstract: Efficient statistical inference on nonignorable missing data is a challenging problem. This paper proposes a new estimation procedure based on composite quantile regression (CQR) for linear regression models with nonignorable missing data, that is applicable even with high-dimensional covariates. A parametric model is assumed for modelling response probability, which is estimated by the empirical likelihood approach. Local identifiability of the proposed strategy is guaranteed on the basis of an instrumental variable approach. A set of data-based adaptive weights constructed via an empirical likelihood method is used to weight CQR functions. The proposed method is resistant to heavy-tailed errors or outliers in the response. An adaptive penalisation method for variable selection is proposed to achieve sparsity with high-dimensional covariates. Limiting distributions of the proposed estimators are derived. Simulation studies are conducted to investigate the finite sample performance of the proposed methodologies. An application to the ACTG 175 data is analysed. Journal: Journal of Nonparametric Statistics Pages: 189-212 Issue: 2 Volume: 29 Year: 2017 Month: 4 X-DOI: 10.1080/10485252.2017.1285030 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1285030 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:189-212 Template-Type: ReDIF-Article 1.0 Author-Name: Jyh-Shyang Wu Author-X-Name-First: Jyh-Shyang Author-X-Name-Last: Wu Author-Name: Wen-Shuenn Deng Author-X-Name-First: Wen-Shuenn Author-X-Name-Last: Deng Title: A nonparametric procedure for testing partially ranked data Abstract: In consumer preference studies, it is common to seek a complete ranking of a variety of, say N, alternatives or treatments. Unfortunately, as N increases, it becomes progressively more confusing and undesirable for respondents to rank all N alternatives simultaneously. Moreover, the investigators may only be interested in consumers’ top few choices. Therefore, it is desirable to accommodate the setting where each survey respondent ranks only her/his most preferred k (k < N) alternatives. In this paper, we propose a simple procedure to test the independence of N alternatives and the top-k ranks, such that the value of k can be predetermined before securing a set of partially ranked data or be at the discretion of the investigator in the presence of complete ranking data. The asymptotic distribution of the proposed test under root-n local alternatives is established. We demonstrate our procedure with two real data sets. Journal: Journal of Nonparametric Statistics Pages: 213-230 Issue: 2 Volume: 29 Year: 2017 Month: 4 X-DOI: 10.1080/10485252.2017.1303055 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1303055 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:213-230 Template-Type: ReDIF-Article 1.0 Author-Name: Jinguo Gao Author-X-Name-First: Jinguo Author-X-Name-Last: Gao Author-Name: Omer Ozturk Author-X-Name-First: Omer Author-X-Name-Last: Ozturk Title: Rank regression in order restricted randomised designs Abstract: This paper uses order restricted randomised design (ORRD) to create a judgment ranked blocking factor based on available subjective information in a small set of experimental units (EUs). The design then performs a carefully designed randomisation scheme with certain restriction to assign the treatment levels to EUs across these subjective judgment blocks. Such an assignment induces positive dependence among within-set units, and the restrictions on the randomisation translate this positive dependence into a variance reduction technique. We provide a unified theory to analyse the data sets collected from an ORRD. The analysis uses the general framework of rank regression methodology in linear models, with some modification to our randomisation scheme, to estimate regression parameter and to test general linear hypotheses. It is shown that the estimators and test statistics have limiting normal and chi-square distributions regardless the quality of ranking information. A simulation study shows that the asymptotic results remain valid even for relatively small sample sizes. The proposed tests are applied to a clinical trial data set. Journal: Journal of Nonparametric Statistics Pages: 231-257 Issue: 2 Volume: 29 Year: 2017 Month: 4 X-DOI: 10.1080/10485252.2017.1303056 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1303056 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:231-257 Template-Type: ReDIF-Article 1.0 Author-Name: Yuping Chen Author-X-Name-First: Yuping Author-X-Name-Last: Chen Author-Name: Yang Bai Author-X-Name-First: Yang Author-X-Name-Last: Bai Author-Name: Wingkam Fung Author-X-Name-First: Wingkam Author-X-Name-Last: Fung Title: Structural identification and variable selection in high-dimensional varying-coefficient models Abstract: Varying-coefficient models have been widely used to investigate the possible time-dependent effects of covariates when the response variable comes from normal distribution. Much progress has been made for inference and variable selection in the framework of such models. However, the identification of model structure, that is how to identify which covariates have time-varying effects and which have fixed effects, remains a challenging and unsolved problem especially when the dimension of covariates is much larger than the sample size. In this article, we consider the structural identification and variable selection problems in varying-coefficient models for high-dimensional data. Using a modified basis expansion approach and group variable selection methods, we propose a unified procedure to simultaneously identify the model structure, select important variables and estimate the coefficient curves. The unique feature of the proposed approach is that we do not have to specify the model structure in advance, therefore, it is more realistic and appropriate for real data analysis. Asymptotic properties of the proposed estimators have been derived under regular conditions. Furthermore, we evaluate the finite sample performance of the proposed methods with Monte Carlo simulation studies and a real data analysis. Journal: Journal of Nonparametric Statistics Pages: 258-279 Issue: 2 Volume: 29 Year: 2017 Month: 4 X-DOI: 10.1080/10485252.2017.1303057 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1303057 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:258-279 Template-Type: ReDIF-Article 1.0 Author-Name: A. K. M. Fazlur Rahman Author-X-Name-First: A. K. M. Fazlur Author-X-Name-Last: Rahman Author-Name: Limin Peng Author-X-Name-First: Limin Author-X-Name-Last: Peng Author-Name: Amita Manatunga Author-X-Name-First: Amita Author-X-Name-Last: Manatunga Author-Name: Ying Guo Author-X-Name-First: Ying Author-X-Name-Last: Guo Title: Nonparametric regression method for broad sense agreement Abstract: Characterising the correspondence between an ordinal measurement and a continuous measurement is often of interest in mental health studies. To this end Peng et al. [(2011), ‘A Framework for Assessing Broad Sense Agreement Between Ordinal and Continuous Measurements’, Journal of the American Statistical Association, 106, 1592–1601] introduced the concept of broad sense agreement (BSA) and developed nonparametric estimation and inference for a BSA measure. In this work, we propose a nonparametric regression framework for BSA, which provides a robust tool to further investigate population heterogeneity in BSA. We develop inferential procedures including regression function estimation and hypothesis testing. Extensive simulation studies demonstrate satisfactory performance of the proposed method. We also apply the new method to a recent Grady Trauma Study and reveal an interesting impact of depression severity on the alignment between a self-reported symptom instrument and clinician diagnosis in posttraumatic stress disorder patients. Journal: Journal of Nonparametric Statistics Pages: 280-300 Issue: 2 Volume: 29 Year: 2017 Month: 4 X-DOI: 10.1080/10485252.2017.1303058 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1303058 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:280-300 Template-Type: ReDIF-Article 1.0 Author-Name: Z. Guessoum Author-X-Name-First: Z. Author-X-Name-Last: Guessoum Author-Name: F. Hamrani Author-X-Name-First: F. Author-X-Name-Last: Hamrani Title: Convergence rate of the kernel regression estimator for associated and truncated data Abstract: This paper studies the behaviour of the kernel estimator of the regression function for associated data in the random left truncated model. The uniform strong consistency rate over a real compact set of the estimate is established. The finite sample performance of the estimator is investigated through extensive simulation studies. Journal: Journal of Nonparametric Statistics Pages: 425-446 Issue: 2 Volume: 29 Year: 2017 Month: 4 X-DOI: 10.1080/10485252.2017.1303059 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1303059 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:425-446 Template-Type: ReDIF-Article 1.0 Author-Name: Xianzheng Huang Author-X-Name-First: Xianzheng Author-X-Name-Last: Huang Author-Name: Haiming Zhou Author-X-Name-First: Haiming Author-X-Name-Last: Zhou Title: An alternative local polynomial estimator for the error-in-variables problem Abstract: We consider the problem of estimating a regression function when a covariate is measured with error. Using the local polynomial estimator of Delaigle et al. [(2009), ‘A Design-adaptive Local Polynomial Estimator for the Errors-in-variables Problem’, Journal of the American Statistical Association, 104, 348–359] as a benchmark, we propose an alternative way of solving the problem without transforming the kernel function. The asymptotic properties of the alternative estimator are rigorously studied. A detailed implementing algorithm and a computationally efficient bandwidth selection procedure are also provided. The proposed estimator is compared with the existing local polynomial estimator via extensive simulations and an application to the motorcycle crash data. The results show that the new estimator can be less biased than the existing estimator and is numerically more stable. Journal: Journal of Nonparametric Statistics Pages: 301-325 Issue: 2 Volume: 29 Year: 2017 Month: 4 X-DOI: 10.1080/10485252.2017.1303060 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1303060 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:301-325 Template-Type: ReDIF-Article 1.0 Author-Name: Marie Hušková Author-X-Name-First: Marie Author-X-Name-Last: Hušková Author-Name: Matúš Maciak Author-X-Name-First: Matúš Author-X-Name-Last: Maciak Title: Discontinuities in robust nonparametric regression with α-mixing dependence Abstract: The main idea of the paper is to introduce a robust regression estimation method under an α-mixing dependence assumption, staying free of any parametric model restrictions while also allowing for some sudden changes in the unknown regression function. The sudden changes in the model may correspond to discontinuity points (jumps) or higher order breaks (jumps in corresponding derivatives) as well. We firstly derive some important statistical properties for local polynomial M-smoother estimates and we will propose a statistical test to decide whether some given point of interest is significantly important for a change to occur or not. As the asymptotic distribution of the test statistic depends on quantities which are left unknown we also introduce a bootstrap algorithm which can be used to mimic the target distribution of interest. All necessary proofs are provided together with some experimental results from a simulation study and a real data example. Journal: Journal of Nonparametric Statistics Pages: 447-475 Issue: 2 Volume: 29 Year: 2017 Month: 4 X-DOI: 10.1080/10485252.2017.1303061 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1303061 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:447-475 Template-Type: ReDIF-Article 1.0 Author-Name: Jianglin Fang Author-X-Name-First: Jianglin Author-X-Name-Last: Fang Author-Name: Wanrong Liu Author-X-Name-First: Wanrong Author-X-Name-Last: Liu Author-Name: Xuewen Lu Author-X-Name-First: Xuewen Author-X-Name-Last: Lu Title: Penalised empirical likelihood for the additive hazards model with high-dimensional data Abstract: In this article, we apply the empirical likelihood (EL) method to the additive hazards model with high-dimensional data and propose the penalised empirical likelihood (PEL) method for parameter estimation and variable selection. It is shown that the estimator based on the EL method has the efficient property, and the limit distribution of the EL ratio statistic for the parameters is a asymptotic normal distribution under the true null hypothesis. In a high-dimensional setting, we prove that the PEL method in the additive hazards model has the oracle property, that is, with probability tending to 1, and the estimator based on the PEL method for the nonzero parameters is estimation and selection consistent if the hypothesised model is true. Moreover, the PEL ratio statistic for the parameters is a $ \chi _{q}^{2} $ χq2 distribution under the true null hypothesis. The performance of the proposed methods is illustrated via a real data application and numerical simulations. Journal: Journal of Nonparametric Statistics Pages: 326-345 Issue: 2 Volume: 29 Year: 2017 Month: 4 X-DOI: 10.1080/10485252.2017.1303062 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1303062 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:326-345 Template-Type: ReDIF-Article 1.0 Author-Name: M. Belalia Author-X-Name-First: M. Author-X-Name-Last: Belalia Author-Name: T. Bouezmarni Author-X-Name-First: T. Author-X-Name-Last: Bouezmarni Author-Name: F. C. Lemyre Author-X-Name-First: F. C. Author-X-Name-Last: Lemyre Author-Name: A. Taamouti Author-X-Name-First: A. Author-X-Name-Last: Taamouti Title: Testing independence based on Bernstein empirical copula and copula density Abstract: In this paper we provide three nonparametric tests of independence between continuous random variables based on the Bernstein copula distribution function and the Bernstein copula density function. The first test is constructed based on a Cramér-von Mises divergence-type functional based on the empirical Bernstein copula process. The two other tests are based on the Bernstein copula density and use Cramér-von Mises and Kullback–Leibler divergence-type functionals, respectively. Furthermore, we study the asymptotic null distribution of each of these test statistics. Finally, we consider a Monte Carlo experiment to investigate the performance of our tests. In particular we examine their size and power which we compare with those of the classical nonparametric tests that are based on the empirical distribution function. Journal: Journal of Nonparametric Statistics Pages: 346-380 Issue: 2 Volume: 29 Year: 2017 Month: 4 X-DOI: 10.1080/10485252.2017.1303063 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1303063 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:346-380 Template-Type: ReDIF-Article 1.0 Author-Name: Yang Cheng Author-X-Name-First: Yang Author-X-Name-Last: Cheng Author-Name: Bo Huang Author-X-Name-First: Bo Author-X-Name-Last: Huang Author-Name: Zhou Yu Author-X-Name-First: Zhou Author-X-Name-Last: Yu Title: A note on iterative AK composite estimator for Current Population Survey Abstract: In this article, we introduce the iterative AK composite estimator for the Current Population Survey. This estimator adopts the AK composite estimator as the initial value and further makes good use of the intrinsic composite scheme of the AK composite estimator. We derive the mean squared error (MSE) formula for the iterative composite estimator and describe how to select the optimal tuning coefficients by minimising the MSE. Finally, we examine the proposed method through a simulation study. Journal: Journal of Nonparametric Statistics Pages: 381-390 Issue: 2 Volume: 29 Year: 2017 Month: 4 X-DOI: 10.1080/10485252.2017.1303064 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1303064 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:381-390 Template-Type: ReDIF-Article 1.0 Author-Name: I. Gijbels Author-X-Name-First: I. Author-X-Name-Last: Gijbels Author-Name: M. A. Ibrahim Author-X-Name-First: M. A. Author-X-Name-Last: Ibrahim Author-Name: A. Verhasselt Author-X-Name-First: A. Author-X-Name-Last: Verhasselt Title: Shape testing in quantile varying coefficient models with heteroscedastic error Abstract: The interest is in regression quantiles in varying coefficient models for analysing longitudinal data. The coefficients are allowed to vary with time, and the error variance (the variability function) varies with the covariates to allow for heteroscedasticity. The functional coefficients are estimated using penalized splines (P-splines), not requiring specification of the error distribution. A likelihood-ratio-type test is considered to test the shape (constancy, monotonicity and/or convexity) of the functional coefficients. Further, testing procedures based on $ L_1 $ L1-norm, $ L_2 $ L2-norm and $ L_\infty $ L∞-norm of the differences of the P-splines coefficients are considered to test for constant functional coefficients. These norm-based tests perform better than the likelihood-ratio-type test in our simulation study. An extreme value test for testing monotonicity or convexity also performs better than the likelihood-ratio-type test. The likelihood-ratio-type test is, however, useful when testing the shape of the coefficients in signal and in variability function simultaneously. A real-data example demonstrates the testing procedures. Journal: Journal of Nonparametric Statistics Pages: 391-406 Issue: 2 Volume: 29 Year: 2017 Month: 4 X-DOI: 10.1080/10485252.2017.1303066 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1303066 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:391-406 Template-Type: ReDIF-Article 1.0 Author-Name: A. Pini Author-X-Name-First: A. Author-X-Name-Last: Pini Author-Name: S. Vantini Author-X-Name-First: S. Author-X-Name-Last: Vantini Title: Interval-wise testing for functional data Abstract: In the framework of null hypothesis significance testing for functional data, we propose a procedure able to select intervals of the domain imputable for the rejection of a null hypothesis. An unadjusted p-value function and an adjusted one are the output of the procedure, namely interval-wise testing. Depending on the sort and level α of type-I error control, significant intervals can be selected by thresholding the two p-value functions at level α. We prove that the unadjusted (adjusted) p-value function point-wise (interval-wise) controls the probability of type-I error and it is point-wise (interval-wise) consistent. To enlighten the gain in terms of interpretation of the phenomenon under study, we applied the interval-wise testing to the analysis of a benchmark functional data set, i.e. Canadian daily temperatures. The new procedure provides insights that current state-of-the-art procedures do not, supporting similar advantages in the analysis of functional data with less prior knowledge. Journal: Journal of Nonparametric Statistics Pages: 407-424 Issue: 2 Volume: 29 Year: 2017 Month: 4 X-DOI: 10.1080/10485252.2017.1306627 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1306627 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:407-424 Template-Type: ReDIF-Article 1.0 Author-Name: Omer Ozturk Author-X-Name-First: Omer Author-X-Name-Last: Ozturk Title: Nonparametric maximum-likelihood estimation of within-set ranking errors in ranked set sampling Abstract: A distribution-free statistical inference for the quality of within-set judgement ranking information is developed for ranked set samples. The judgement ranking information is modelled through Bohn–Wolfe (BW) model. The cumulative distribution function and the parameters of BW model are estimated by maximising nonparametric likelihood functions. A missing data model is introduced to construct an efficient computational algorithm. The advantages of the new estimators are that they require essentially no assumption on the underlying distribution function, which provides an estimate of the quality of within-set ranking information, and that they lead to a valid statistical inference even under imperfect ranking. The proposed estimators are applied to a water flow data set to estimate judgement ranking information and underlying distribution function. Journal: Journal of Nonparametric Statistics Pages: 823-840 Issue: 7 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903287914 File-URL: http://hdl.handle.net/10.1080/10485250903287914 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:7:p:823-840 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Serfling Author-X-Name-First: Robert Author-X-Name-Last: Serfling Title: Equivariance and invariance properties of multivariate quantile and related functions, and the role of standardisation Abstract: Equivariance and invariance issues arise as a fundamental but often problematic aspect of multivariate statistical analysis. For multivariate quantile and related functions, we provide coherent definitions of these properties. For standardisation of multivariate data to produce equivariance or invariance of procedures, three important types of matrix-valued functional are studied: ‘weak covariance’ (or ‘shape’), ‘transformation–retransformation’ (TR), and ‘strong invariant coordinate system’ (SICS). The clarification of TR affine equivariant versions of the sample spatial quantile function is obtained. It is seen that geometric artefacts of SICS-standardised data are invariant under affine transformation of the original data followed by standardisation using the same SICS functional, subject only to translation and homogeneous scale change. Some applications of SICS standardisation are described. Journal: Journal of Nonparametric Statistics Pages: 915-936 Issue: 7 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903431710 File-URL: http://hdl.handle.net/10.1080/10485250903431710 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:7:p:915-936 Template-Type: ReDIF-Article 1.0 Author-Name: Marc Hallin Author-X-Name-First: Marc Author-X-Name-Last: Hallin Author-Name: Davy Paindaveine Author-X-Name-First: Davy Author-X-Name-Last: Paindaveine Author-Name: Thomas Verdebout Author-X-Name-First: Thomas Author-X-Name-Last: Verdebout Title: Testing for Common Principal Components under Heterokurticity Abstract: The so-called common principal components (CPC) model, in which the covariance matrices Σi of m populations are assumed to have identical eigenvectors, was introduced by Flury [Flury, B. (1984), ‘Common Principal Components in k Groups’, Journal of the American Statistical Association, 79, 892–898]. Gaussian parametric inference methods [Gaussian maximum-likelihood estimation and Gaussian likelihood ratio test (LRT)] have been fully developed for this model, but their validity does not extend beyond the case of elliptical densities with common Gaussian kurtosis. A non-Gaussian (but still homokurtic) extension of Flury's Gaussian LRT for the hypothesis of CPC [Flury, B. (1984), ‘Common Principal Components in k Groups’, Journal of the American Statistical Association, 79, 892–898] is proposed in Boik [Boik, J.R. (2002), ‘Spectral Models for Covariance Matrices’, Biometrika, 89, 159–182], see also Boente and Orellana [Boente, G., and Orellana, L. (2001), ‘A Robust Approach to Common Principal Components’, in Statistics in Genetics and in the Environmental Sciences, eds. Sciences Fernholz, S. Morgenthaler, and W. Stahel, Basel: Birkhauser, pp. 117–147] and Boente, Pires and Rodrigues [Boente, G., Pires, A.M., and Rodrigues I.M. (2009), ‘Robust Tests for the Common Principal Components Model’, Journal of Statistical Planning and Inference, 139, 1332–1347] for robust versions. In this paper, we show how Flury's LRT can be modified into a pseudo-Gaussian test which remains valid under arbitrary, hence possibly heterokurtic, elliptical densities with finite fourth-order moments, while retaining its optimality features at the Gaussian. Journal: Journal of Nonparametric Statistics Pages: 879-895 Issue: 7 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903548737 File-URL: http://hdl.handle.net/10.1080/10485250903548737 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:7:p:879-895 Template-Type: ReDIF-Article 1.0 Author-Name: Sam Efromovich Author-X-Name-First: Sam Author-X-Name-Last: Efromovich Author-Name: Zibonele Valdez-Jasso Author-X-Name-First: Zibonele Author-X-Name-Last: Valdez-Jasso Title: Aggregated wavelet estimation and its application to ultra-fast fMRI Abstract: The methodology of aggregation of known nonparametric regression estimators into a single better estimator has received increasing attention in statistical literature. Traditional aggregation means that a linear or convex combination of several estimators is considered. Wavelet regression estimation, due to its multiresolution nature, presents another opportunity for aggregation – using different estimation procedures on different resolution scales. Such an opportunity becomes attractive if known wavelet estimators have desired complementary properties on different frequencies. The difficulty of such an aggregation is that the assignment of scales depends on an underlying regression function and regression errors. This paper proposes a data-driven aggregation of two wavelet estimators – SureBlock of Cai and Zhou [(2009), ‘A Data-driven Block Thresholding Approach to Wavelet Estimation’, Annals of Statistics, 37, 569–595] and Universal of Efromovich [(1999a,b), Nonparametric Curve Estimation: Methods, Theory and Applications, New York: Springer; ‘Quasi-linear Wavelet Estimation’, Journal of the American Statistical Association, 94, 189–204] – to achieve a better quality of estimation, better data-compression, and better visualisation of functions with different smoothness characteristics on low and high frequencies. The proposed estimator is motivated by an applied problem of denoising and compression of ultra-fast (UF) functional magnetic resonance imaging (fMRI) – the new magnetic resonance technology that screens the activity of brain voxels every 50 ms with the purpose of understanding human brain activity. The proposed aggregated wavelet estimator is supported by the asymptotic theory, tested via intensive numerical simulations and UF fMRI applications, and it is expected to be useful in similar applications. Journal: Journal of Nonparametric Statistics Pages: 841-857 Issue: 7 Volume: 22 Year: 2010 X-DOI: 10.1080/10485251003653468 File-URL: http://hdl.handle.net/10.1080/10485251003653468 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:7:p:841-857 Template-Type: ReDIF-Article 1.0 Author-Name: Kimihiro Noguchi Author-X-Name-First: Kimihiro Author-X-Name-Last: Noguchi Author-Name: Yulia Gel Author-X-Name-First: Yulia Author-X-Name-Last: Gel Title: Combination of Levene-type tests and a finite-intersection method for testing equality of variances against ordered alternatives Abstract: The problem of detecting monotonic trends in variances from k samples is widely met in many applications, e.g. finance, economics, medicine, biopharmaceutical, and environmental studies. However, most of the tests for equality of variances against ordered alternatives rely on the assumption of normality and are often non-robust to its violation, which eventually leads to unreliable conclusions. In this paper, we propose a new distribution-free test against trends in variances which is based on a combination of a robust Levene-type approach and a finite-intersection method. The new test can be viewed as a piecewise linear approximation to possibly non-linear dynamics of variances, and hence is applicable to a broad range of alternatives. The new combined procedure yields a more accurate estimate of size and provides a competitive power for a variety of distributions and alternatives. In addition, we develop a modification of the proposed test for unbalanced designs with small sample sizes. We discuss asymptotic properties of the new test and illustrate its applications with simulations and case studies from soil pollution analysis, real estate markets, engineering, and epidemiology. Journal: Journal of Nonparametric Statistics Pages: 897-913 Issue: 7 Volume: 22 Year: 2010 X-DOI: 10.1080/10485251003698505 File-URL: http://hdl.handle.net/10.1080/10485251003698505 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:7:p:897-913 Template-Type: ReDIF-Article 1.0 Author-Name: Weihua Zhou Author-X-Name-First: Weihua Author-X-Name-Last: Zhou Title: A multivariate Wilcoxon regression estimate Abstract: Based on the multivariate spatial rank function introduced by Möttönen and Oja [(1995), ‘Multivariate Spatial Sign and Rank Methods’, Journal of Nonparametric Statistics, 5, 201–213] and Möttönen et al. [(1997), ‘On the Efficiency of Multivariate Spatial Sign and Rank Tests’, Annals of Statistics, 25, 542–552], an extension of the univariate Wilcoxon regression estimate to multivariate linear models is proposed and studied. For both of the cases covariates are deterministic and i.i.d. random: we show that the proposed estimate is consistent and asymptotically normal under some appropriate assumptions. We have demonstrated that the asymptotic relative efficiency of the new regression estimate is the same as that of the generalised multivariate Hodges–Lehmann location estimates proposed by Chaudhuri [(1992), ‘Multivariate Location Estimation Using Extension of R-estimates Through U-statistics Type Approach’, Annals of Statistics, 20, 897–916] (with m=2); thus it possesses high efficiency. Simulations show that it also performs very well in the finite sample data. While the estimate is only rotation invariant, a version that is affine invariant is proposed as well. Journal: Journal of Nonparametric Statistics Pages: 859-877 Issue: 7 Volume: 22 Year: 2010 X-DOI: 10.1080/10485251003763226 File-URL: http://hdl.handle.net/10.1080/10485251003763226 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:7:p:859-877 Template-Type: ReDIF-Article 1.0 Author-Name: Edgar Brunner Author-X-Name-First: Edgar Author-X-Name-Last: Brunner Author-Name: Madan Puri Author-X-Name-First: Madan Author-X-Name-Last: Puri Author-Name: Robert Serfling Author-X-Name-First: Robert Author-X-Name-Last: Serfling Title: Editorial for the special issue on ‘Papers inspired by the Workshop “Nonparametric Statistics: Refined, Redefined, and Renewed”’ Journal: Pages: 821-822 Issue: 7 Volume: 22 Year: 2010 X-DOI: 10.1080/10485251003773944 File-URL: http://hdl.handle.net/10.1080/10485251003773944 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:7:p:821-822 Template-Type: ReDIF-Article 1.0 Author-Name: M'hamed Ezzahrioui Author-X-Name-First: M'hamed Author-X-Name-Last: Ezzahrioui Author-Name: Elias Ould-Saïd Author-X-Name-First: Elias Author-X-Name-Last: Ould-Saïd Title: Asymptotic normality of a nonparametric estimator of the conditional mode function for functional data Abstract: We consider the estimation of the conditional mode function when the covariables take values in some abstract function space. It is shown that, under some regularity conditions, the kernel estimate of the conditional mode is asymptotically normally distributed. From this, we derive the asymptotic normality of a predictor and propose confidence bands for the conditional mode function. Simulations are drawn to show how our methodology can be implemented. Journal: Journal of Nonparametric Statistics Pages: 3-18 Issue: 1 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250701541454 File-URL: http://hdl.handle.net/10.1080/10485250701541454 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:1:p:3-18 Template-Type: ReDIF-Article 1.0 Author-Name: Qing Kang Author-X-Name-First: Qing Author-X-Name-Last: Kang Author-Name: Paul Nelson Author-X-Name-First: Paul Author-X-Name-Last: Nelson Title: Nonparametric tests for the median from a size-biased sample Abstract: This study explores issues related to one-sample nonparametric tests for the median of a continuous distribution when the sample is collected via size-bias of a known order. A general principle on how to construct the reference distribution of a given test statistic is presented. Following this principle, we create new bias-corrected nonparametric testing procedures. Computationally intensive, exact P-values are available for a small sample. When the sample size is large, P-values can be easily estimated by the asymptotic approximation developed here. Power functions of these tests are investigated in both small- and large-sample cases and consistency is shown to hold under fairly general conditions. The tests’ performances are then compared via asymptotic relative efficiency under four theoretical distributions. Journal: Journal of Nonparametric Statistics Pages: 19-37 Issue: 1 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250701830113 File-URL: http://hdl.handle.net/10.1080/10485250701830113 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:1:p:19-37 Template-Type: ReDIF-Article 1.0 Author-Name: A.E. Gomes Author-X-Name-First: A.E. Author-X-Name-Last: Gomes Title: Consistency of the non-parametric maximum pseudo-likelihood estimator of the disease onset distribution function for a survival–sacrifice model Abstract: Suppose that in a carcinogenicity experiment with animals where the tumour is not palpable, we observe only the time of death of the animal, the cause of death (the tumour or another independent cause, as sacrifice) and whether the tumour was present at the time of death. These last two indicator variables are evaluated after an autopsy. We can estimate the cumulative distribution function F2 of the time of death from the disease using the Kaplan–Meier estimator and then calculate the non-parametric maximum pseudo-likelihood estimator (NPMPLE) of the cumulative distribution function F1 of the time of onset of the disease. After a brief review of some past works on the estimation of F1 and F2, we demonstrate the strong uniform consistency of the NPMPLE of F1. Journal: Journal of Nonparametric Statistics Pages: 39-46 Issue: 1 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250701830121 File-URL: http://hdl.handle.net/10.1080/10485250701830121 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:1:p:39-46 Template-Type: ReDIF-Article 1.0 Author-Name: Fuxia Cheng Author-X-Name-First: Fuxia Author-X-Name-Last: Cheng Title: Asymptotic properties in ARCH(p)-time series Abstract: In this paper we consider the asymptotic distributions of the innovation density estimators in ARCH(p)-time series. We first obtain the asymptotic normality of the innovation density estimator at a fixed point. Globally, we show that the asymptotic distribution of the maximum of a suitably normalized deviation of the innovation density estimator from the expectation of the kernel innovation density (based on the true innovation) is the same as in the case of the one sample set up, which was given by Bickel and Rosenblatt [P.J. Bickel and M. Rosenblatt, On some global measures of the deviations of density function estimators, Ann. Statist. 6 (1973), pp. 1071–1095]. Journal: Journal of Nonparametric Statistics Pages: 47-60 Issue: 1 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250701830139 File-URL: http://hdl.handle.net/10.1080/10485250701830139 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:1:p:47-60 Template-Type: ReDIF-Article 1.0 Author-Name: Jiti Gao Author-X-Name-First: Jiti Author-X-Name-Last: Gao Author-Name: Yongmiao Hong Author-X-Name-First: Yongmiao Author-X-Name-Last: Hong Title: Central limit theorems for generalized -statistics with applications in nonparametric specification Abstract: In this paper, we establish some new central limit theorems for generalized U-statistics of dependent processes under some mild conditions. Such central limit theorems complement existing results available from both the econometrics literature and statistics literature. We then look at applications of the established results to a number of test problems in time series regression models. Journal: Journal of Nonparametric Statistics Pages: 61-76 Issue: 1 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250801899596 File-URL: http://hdl.handle.net/10.1080/10485250801899596 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:1:p:61-76 Template-Type: ReDIF-Article 1.0 Author-Name: Ansa Alphonsa Antony Author-X-Name-First: Ansa Author-X-Name-Last: Alphonsa Antony Author-Name: P.G. Sankaran Author-X-Name-First: P.G. Author-X-Name-Last: Sankaran Title: Nonparametric estimation of bivariate survivor function under masked causes of failure Abstract: Consider a system that consists of k components. Each component is subject to more than one cause of failure. Due to inadequacy in the diagnostic mechanism or reluctance to report any specific cause of failure (disease), the exact cause of failure cannot be identified easily. In such situations, where the cause of failure is masked, test procedures restrict the cause of failure to a set of possible types containing the true failure cause. In this paper, we develop a nonparametric estimator for the bivariate survivor function of competing risk models under masked causes of failure based on the vector hazard rate. Asymptotic properties of the estimator are established. A simulation study is carried out to assess the performance of the estimator. We also illustrate the method with a data set. Journal: Journal of Nonparametric Statistics Pages: 77-89 Issue: 1 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250801905872 File-URL: http://hdl.handle.net/10.1080/10485250801905872 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:1:p:77-89 Template-Type: ReDIF-Article 1.0 Author-Name: Manuel Úbeda-Flores Author-X-Name-First: Manuel Author-X-Name-Last: Úbeda-Flores Title: Multivariate copulas with cubic sections in one variable Abstract: In this paper, we construct and characterise multivariate copulas with cubic sections in one variable. We also study some of their properties: ordering, dependence concepts, and a measure of multivariate association. Several examples illustrate our results. Journal: Journal of Nonparametric Statistics Pages: 91-98 Issue: 1 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250801908355 File-URL: http://hdl.handle.net/10.1080/10485250801908355 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:1:p:91-98 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Editorial Journal: Pages: 1-2 Issue: 1 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250801956677 File-URL: http://hdl.handle.net/10.1080/10485250801956677 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:1:p:1-2 Template-Type: ReDIF-Article 1.0 Author-Name: Hammou El Barmi Author-X-Name-First: Hammou Author-X-Name-Last: El Barmi Author-Name: Dobrin Marchev Author-X-Name-First: Dobrin Author-X-Name-Last: Marchev Title: New and improved estimators of distribution functions under second-order stochastic dominance Abstract: Second-order stochastic ordering plays a fundamental role in many scientific areas including economics and finance. This article is concerned with the estimation of two continuous distribution functions, F1 and F2, when F1 is smaller than F2 according to this ordering. In the one-sample case, we assume that F1 is known and provide a uniformly consistent estimator for F2. The problem of estimating F1 when F2 is known was considered in Rojo and El Barmi [J. Rojo and H. El Barmi, Estimation of distribution functions under second order stochastic dominance, Statist. Sinica 13 (2003), pp. 903–926]. For this case, we show that their estimator continues to be uniformly strongly consistent without the restrictive conditions that they impose on F1. In the two-sample case, we propose a new class of uniformly strongly consistent estimators for the two distribution functions, where n1 and n2 are the sample sizes. An extensive simulation study shows that for α = n1/(n1+n2), the new estimators outperform those proposed by Rojo and El Barmi [J. Rojo and H. El Barmi, Estimation of distribution functions under second order stochastic dominance, Statist. Sinica 13 (2003), pp. 903–926] for the two-sample case in terms of mean squared error at most of the quantiles of the distributions that we consider. An example is discussed to illustrate the theoretical results. Journal: Journal of Nonparametric Statistics Pages: 143-153 Issue: 2 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802322390 File-URL: http://hdl.handle.net/10.1080/10485250802322390 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:2:p:143-153 Template-Type: ReDIF-Article 1.0 Author-Name: M. Akritas Author-X-Name-First: M. Author-X-Name-Last: Akritas Author-Name: A. Stavropoulos Author-X-Name-First: A. Author-X-Name-Last: Stavropoulos Author-Name: C. Caroni Author-X-Name-First: C. Author-X-Name-Last: Caroni Title: Asymptotic theory of weighted -statistics based on ranks Abstract: Using subspaces to describe the nonparametric null hypotheses introduced in Akritas and Arnold [Fully nonparametric hypotheses for factorial designs I: multivariate repeated measures designs, J. Amer. Statist. Assoc. 89 (1994), pp. 336–343.], leads to a natural extension of the models and the class of nonparametric hypotheses considered there. Nonparametric versions of all saturated or unsaturated parametric models for factorial designs, as well as nonparametric versions of all parametric hypotheses considered in such contexts, are included in the new formulation. To test these new hypotheses we introduce a new family of (mid-)rank statistics. The new statistics are modelled after the weighted F-statistics and are appropriate for (possibly) unbalanced designs with independent observations that can be heteroscedastic. Being rank versions of likelihood ratio statistics, the proposed statistics apply in situations where the Wald-type rank statistics of Akritas, Arnold and Brunner [Nonparametric hypotheses and rank statistics for unbalanced factorial designs, J. Amer. Statist. Assoc. 92 (1997), pp. 258–265.] have not been extended and are at least as efficient in the cases where both apply. We show that the new rank statistics converge in distribution to central chi-squared distributions under their respective null hypotheses. Finding the asymptotic distribution of statistics without a closed form expression requires a novel approach, which we introduce. A simulation study compares the achieved level and power of the new statistics with a number of competing procedures. Journal: Journal of Nonparametric Statistics Pages: 177-191 Issue: 2 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802485528 File-URL: http://hdl.handle.net/10.1080/10485250802485528 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:2:p:177-191 Template-Type: ReDIF-Article 1.0 Author-Name: Alexandre Leblanc Author-X-Name-First: Alexandre Author-X-Name-Last: Leblanc Title: Chung–Smirnov property for Bernstein estimators of distribution functions Abstract: In this article, we show that the Chung–Smirnov property holds for Bernstein estimators of distribution functions under different conditions on the underlying distribution to be estimated. In doing so, we obtain general results that characterise the closeness between these Bernstein estimators and the empirical distribution function Fn. Journal: Journal of Nonparametric Statistics Pages: 133-142 Issue: 2 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802485676 File-URL: http://hdl.handle.net/10.1080/10485250802485676 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:2:p:133-142 Template-Type: ReDIF-Article 1.0 Author-Name: Seija Sirkiä Author-X-Name-First: Seija Author-X-Name-Last: Sirkiä Author-Name: Sara Taskinen Author-X-Name-First: Sara Author-X-Name-Last: Taskinen Author-Name: Hannu Oja Author-X-Name-First: Hannu Author-X-Name-Last: Oja Author-Name: David Tyler Author-X-Name-First: David Author-X-Name-Last: Tyler Title: Tests and estimates of shape based on spatial signs and ranks Abstract: Nonparametric procedures for testing and estimation of the shape matrix in the case of multivariate elliptic distribution are considered. Testing for sphericity is an important special case. The tests and estimates are based on the spatial sign and rank covariance matrices. The estimates based on the spatial sign covariance matrix and symmetrized spatial sign covariance matrix are Tyler's [A distribution-free M-estimator of multivariate scatter, Ann. Statist. 15 (1987), pp. 234–251] shape matrix and and Dümbgen's [On Tyler's M-functional of scatter in high dimension, Ann. Inst. Statist. Math. 50 (1998), pp. 471–491] shape matrix, respectively. The test based on the spatial sign covariance matrix is the sign test statistic in the class of nonparametric tests proposed by Hallin and Paindaveine [Semiparametrically efficient rank-based inference for shape. I. Optimal rank-based tests for sphericity, Ann. Statist. 34 (2006), pp. 2707–2756]. New tests and estimates based on the spatial rank covariance matrix are proposed. The shape estimates introduced in the paper play an important role in the inner standardisation of the spatial sign and rank tests for multivariate location. Limiting distributions of the tests and estimates are reviewed and derived, and asymptotic efficiencies as well as finite-sample efficiencies of the proposed tests are compared with those of the classical modified John's [Some optimal multivariate tests, Biometrika 58 (1971), pp. 123–127; The distribution of a statistic used for testing sphericity of normal distributions, Biometrika 59 (1972), pp. 169–173] test and the van der Waerden test (Hallin and Paindaveine, [Semiparametrically efficient rank-based inference for shape. I. Optimal rank-based tests for sphericity, Ann. Statist. 34 (2006), pp. 2707–2756]). The symmetrised spatial sign- and rank-based estimates and tests seem to have a very high efficiency in the multivariate normal case, and they are much better than the classical estimate (shape matrix based on the regular covariance matrix) and test (John's test) for distributions with heavy tails. Journal: Journal of Nonparametric Statistics Pages: 155-176 Issue: 2 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802495691 File-URL: http://hdl.handle.net/10.1080/10485250802495691 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:2:p:155-176 Template-Type: ReDIF-Article 1.0 Author-Name: Estela Dagum Author-X-Name-First: Estela Author-X-Name-Last: Dagum Author-Name: Alessandra Luati Author-X-Name-First: Alessandra Author-X-Name-Last: Luati Title: A note on the statistical properties of nonparametric trend estimators by means of smoothing matrices Abstract: Smoothing matrices associated with linear filters for the estimation of time series’ unobserved components differ from those used in linear regression or generalised additive models due to asymmetry. In fact, while projection smoother matrices are in general symmetric, filtering matrices are not. It follows that many inferential properties developed for symmetric projection matrices no longer hold for time-series smoothing matrices. However, the latter have a well-defined algebraic structure that allows one to derive many properties useful for inference in smoothing problems.In this note, some properties of symmetric smoother matrices are extended to centrosymmetric smoothing matrices. A decomposition of smoothing matrices in submatrices associated with the symmetric and asymmetric components of a filter enables us to consider the different assumptions that characterise estimation in the interior and at the boundaries of a finite time series.Matrix-based measures are defined to approximate the bias and the variance of a trend estimator, both in the interior and at the boundaries. These measures do not depend on the data and provide useful information on the bias–variance trade-off that affects non-parametric estimators. Journal: Journal of Nonparametric Statistics Pages: 193-205 Issue: 2 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802534986 File-URL: http://hdl.handle.net/10.1080/10485250802534986 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:2:p:193-205 Template-Type: ReDIF-Article 1.0 Author-Name: Ao Yuan Author-X-Name-First: Ao Author-X-Name-Last: Yuan Title: Semiparametric inference with kernel likelihood Abstract: We study a class of semiparametric likelihood models in which parameters are incorporated explicitly, with the unknown likelihood specified nonparametrically by the kernel estimator. The maximum likelihood estimator (MLE) under this semiparametric model is used for inference of the parameters. The method is a generalisation of the semiparametric regression model we proposed recently. Such semiparametric models are robust, and MLEs under these likelihoods are shown to be consistent, asymptotic normal with rate √n and possess Wilks property. Journal: Journal of Nonparametric Statistics Pages: 207-228 Issue: 2 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802553382 File-URL: http://hdl.handle.net/10.1080/10485250802553382 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:2:p:207-228 Template-Type: ReDIF-Article 1.0 Author-Name: Marco Di Marzio Author-X-Name-First: Marco Author-X-Name-Last: Di Marzio Author-Name: Charles Taylor Author-X-Name-First: Charles Author-X-Name-Last: Taylor Title: Using small bias nonparametric density estimators for confidence interval estimation Abstract: Confidence intervals for densities built on the basis of standard nonparametric theory are doomed to have poor coverage rates due to bias. Studies on coverage improvement exist, but reasonably behaved interval estimators are needed. We explore the use of small bias kernel-based methods to construct confidence intervals, in particular using a geometric density estimator that seems better suited for this purpose. Journal: Journal of Nonparametric Statistics Pages: 229-240 Issue: 2 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802562607 File-URL: http://hdl.handle.net/10.1080/10485250802562607 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:2:p:229-240 Template-Type: ReDIF-Article 1.0 Author-Name: Jung Park Author-X-Name-First: Jung Author-X-Name-Last: Park Author-Name: Marc Genton Author-X-Name-First: Marc Author-X-Name-Last: Genton Author-Name: Sujit Ghosh Author-X-Name-First: Sujit Author-X-Name-Last: Ghosh Title: Nonparametric autocovariance estimation from censored time series by Gaussian imputation Abstract: One of the most frequently used methods to model the autocovariance function of a second-order stationary time series is to use the parametric framework of autoregressive and moving average models developed by Box and Jenkins. However, such parametric models, though very flexible, may not always be adequate to model autocovariance functions with sharp changes. Furthermore, if the data do not follow the parametric model and are censored at a certain value, the estimation results may not be reliable. We develop a Gaussian imputation method to estimate an autocovariance structure via nonparametric estimation of the autocovariance function in order to address both censoring and incorrect model specification. We demonstrate the effectiveness of the technique in terms of bias and efficiency with simulations under various rates of censoring and underlying models. We describe its application to a time series of silicon concentrations in the Arctic. Journal: Journal of Nonparametric Statistics Pages: 241-259 Issue: 2 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802570964 File-URL: http://hdl.handle.net/10.1080/10485250802570964 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:2:p:241-259 Template-Type: ReDIF-Article 1.0 Author-Name: Dimitrios Bagkavos Author-X-Name-First: Dimitrios Author-X-Name-Last: Bagkavos Title: Erratum Journal: Pages: 261-261 Issue: 2 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802670202 File-URL: http://hdl.handle.net/10.1080/10485250802670202 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:2:p:261-261 Template-Type: ReDIF-Article 1.0 Author-Name: Junyong Park Author-X-Name-First: Junyong Author-X-Name-Last: Park Title: Nonparametric empirical Bayes estimator in simultaneous estimation of Poisson means with application to mass spectrometry data Abstract: We consider the problem of simultaneous Poisson mean vector estimation and discuss the performance of nonparametric empirical Bayes (NPEB) estimator from the view point of risk consistency. We define the structural uniform risk consistency with respect to some classes of priors and show that the NPEB estimator achieves a structural uniform risk consistency with respect to some class of priors. It is shown that the NPEB estimator performs better than the maximum-likelihood estimator (MLE) and James–Stein estimators from the view point of structural uniform risk consistency. We also present numerical studies which support the asymptotic results and compare with the MLE and James–Stein-type estimators. We provide a real example of mass spectrometry data from a breast cancer study in Sauter et al. [Sauter, E.R., Davis, W., Qin, W., Scanlon, S., Mooney, B., Bromert, K., and Folk, W.R. (2009), ‘Identification of a β-Casein-Like Peptide in Breast Nipple Aspirate Fluid that is Associated with Breast Cancer’, Biomarkers in Medicine, 3, 577–588] with comparison of various estimators. Journal: Journal of Nonparametric Statistics Pages: 245-265 Issue: 1 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.591396 File-URL: http://hdl.handle.net/10.1080/10485252.2011.591396 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:245-265 Template-Type: ReDIF-Article 1.0 Author-Name: Xuewen Lu Author-X-Name-First: Xuewen Author-X-Name-Last: Lu Author-Name: Heng Lian Author-X-Name-First: Heng Author-X-Name-Last: Lian Author-Name: Wanrong Liu Author-X-Name-First: Wanrong Author-X-Name-Last: Liu Title: Semiparametric estimation for inverse density weighted expectations when responses are missing at random Abstract: When responses are missing at random, we consider semiparametric estimation of inverse density weighted expectations, or equivalently, integrals of conditional expectations. An inverse probability weighted estimator and a full propensity score weighted estimator are proposed and shown to be asymptotically normal. The two estimators are asymptotically equivalent and achieve the semiparametric efficiency bound. The performances of the estimators are investigated and compared with simulation studies and a real data example. Journal: Journal of Nonparametric Statistics Pages: 139-152 Issue: 1 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.599385 File-URL: http://hdl.handle.net/10.1080/10485252.2011.599385 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:139-152 Template-Type: ReDIF-Article 1.0 Author-Name: Alexander Nazarov Author-X-Name-First: Alexander Author-X-Name-Last: Nazarov Author-Name: Natalia Stepanova Author-X-Name-First: Natalia Author-X-Name-Last: Stepanova Title: An extremal problem with applications to the problem of testing multivariate independence Abstract: Some problems of statistics can be reduced to extremal problems of minimizing functionals of smooth functions defined on the cube [0, 1]m, m≥2. In this paper, we study a class of extremal problems that is closely connected to the problem of testing multivariate independence. By solving the extremal problem, we provide a unified approach to establishing weak convergence for a wide class of empirical processes which emerge in connection with testing independence. The use of our result is also illustrated by describing the domain of local asymptotic optimality of some nonparametric tests of independence. Journal: Journal of Nonparametric Statistics Pages: 3-17 Issue: 1 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.603831 File-URL: http://hdl.handle.net/10.1080/10485252.2011.603831 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:3-17 Template-Type: ReDIF-Article 1.0 Author-Name: Min Hee Kim Author-X-Name-First: Min Author-X-Name-Last: Hee Kim Author-Name: Michael Akritas Author-X-Name-First: Michael Author-X-Name-Last: Akritas Title: Goodness-of-fit testing: the thresholding approach Abstract: The classical Pearson's chi-square test for goodness-of-fit has found extensive applications in areas such as contingency tables and, recently, multiple testing. Mann and Wald [(1942), ‘On the Choice of the Number of Class Intervals in the Application of the Chi Square Test’, The Annals of Mathematical Statistics, 13, 306–317] were the first to establish the power advantages of letting the number nbin of bins tend to infinity with n, and found nbin=n2/5 to be the optimal rate. For a corresponding development in the area of contingency tables, see Holst [(1972), ‘Asymptotic Normality and Efficiency for Certain Goodness-of-Fit Tests’, Biometrika, 59, 137–145], Morris [(1975), ‘Central Limit Theorems for Multinomial Sums’, The Annals of Statistics, 3, 165–188], and Koehler and Larntz [(1980), ‘An Empirical Investigation of Goodness-of-Fit Statistics for Sparse Multinomials’, Journal of the American Statistical Association, 75, 336–344]. In this paper, we consider the use of thresholding methods to further improve on the power of Pearson's chi-square test. An alternative statistic, based on the cell averages, is also studied. The Fourier or wavelet transformation is used to ensure power enhancement in both high- and low-signal-to-noise ratio alternatives. Simulations suggest that application of order thresholding (Kim, M.H., and Akritas, M.G. (2010), ‘Order Thresholding’, The Annals of Statistics, 38, 2314–2350) achieves accurate type I error rates, and competitive power. Journal: Journal of Nonparametric Statistics Pages: 119-138 Issue: 1 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.606367 File-URL: http://hdl.handle.net/10.1080/10485252.2011.606367 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:119-138 Template-Type: ReDIF-Article 1.0 Author-Name: David Hunter Author-X-Name-First: David Author-X-Name-Last: Hunter Author-Name: Derek Young Author-X-Name-First: Derek Author-X-Name-Last: Young Title: Semiparametric mixtures of regressions Abstract: We present an algorithm for estimating parameters in a mixture-of-regressions model in which the errors are assumed to be independent and identically distributed but no other assumption is made. This model is introduced as one of several recent generalizations of the standard fully parametric mixture of linear regressions in the literature. A sufficient condition for the identifiability of the parameters is stated and proved. Several different versions of the algorithm, including one that has a provable ascent property, are introduced. Numerical tests indicate the effectiveness of some of these algorithms. Journal: Journal of Nonparametric Statistics Pages: 19-38 Issue: 1 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.608430 File-URL: http://hdl.handle.net/10.1080/10485252.2011.608430 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:19-38 Template-Type: ReDIF-Article 1.0 Author-Name: Jyh-Shyang Wu Author-X-Name-First: Jyh-Shyang Author-X-Name-Last: Wu Author-Name: Wen-Shuenn Deng Author-X-Name-First: Wen-Shuenn Author-X-Name-Last: Deng Title: Averaged shifted chi-square test Abstract: A simple procedure based on the average of shifted chi-square statistics (ASCS) is proposed to improve the classical chi-square procedure for testing whether a random sample has been drawn from a specified continuous distribution. We repeatedly partition the sample space, say, ℓ times to obtain ℓ respective chi-square statistics. The proposed test statistic is defined as the average value of the resultant ℓ shifted chi-square statistics. We prove that the ASCS is asymptotically distributed as a weighted sum of a finite number of chi-square variables by the theory of U-statistics. The proposed procedure is shown to be markedly less sensitive to the choice of the anchor position and Monte Carlo experiments demonstrate that it leads to noticeable gains in power. Journal: Journal of Nonparametric Statistics Pages: 39-57 Issue: 1 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.608849 File-URL: http://hdl.handle.net/10.1080/10485252.2011.608849 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:39-57 Template-Type: ReDIF-Article 1.0 Author-Name: Hongxia Wang Author-X-Name-First: Hongxia Author-X-Name-Last: Wang Author-Name: Jinde Wang Author-X-Name-First: Jinde Author-X-Name-Last: Wang Author-Name: Bo Huang Author-X-Name-First: Bo Author-X-Name-Last: Huang Title: Prediction for spatio-temporal models with autoregression in errors Abstract: In various environmental studies spatio-temporal correlated data are involved, so there has been an increasing demand for spatio-temporal prediction methods that capture spatio-temporal correlation so as to improve the accuracy of prediction. In this paper we propose a nonparametric iteration procedure for spatio-temporal models with specific autocorrelation structures. We extended the local linear method for spatial data to spatio-temporal local linear models, taking both spatial and temporal characteristics into consideration. The asymptotic normality of the predictors is established under mild conditions. The results of a simulation and case study also show that our predictors perform better than the traditional local linear method. Journal: Journal of Nonparametric Statistics Pages: 217-244 Issue: 1 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.616893 File-URL: http://hdl.handle.net/10.1080/10485252.2011.616893 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:217-244 Template-Type: ReDIF-Article 1.0 Author-Name: Yichuan Zhao Author-X-Name-First: Yichuan Author-X-Name-Last: Zhao Author-Name: Song Yang Author-X-Name-First: Song Author-X-Name-Last: Yang Title: Empirical likelihood confidence intervals for regression parameters of the survival rate Abstract: The survival probability of patients plays an important role in biomedical settings. Based on the Jung [(1996), ‘Regression Analysis for Long-Term Survival Rate’, Biometrika, 83, 227–232] regression model for survival probability, Zhao [(2005), ‘Regression Analysis for Long-Term Survival Rate Via Empirical Likelihood’, Journal of Nonparametric Statistics, 17, 995–1007] developed an empirical likelihood (EL) confidence region for the vector of regression parameters. However, the proposed EL method does not work for a subset of regression parameters. In this paper, we develop EL confidence regions for any subset or a linear combination of the vectors of the regression parameters under the regression model. We propose two kinds of confidence intervals for the survival rate of a patient with the given covariates. A simulation study is carried out to compare the proposed method with the normal approximation-based method and nonparametric bootstrap method. Finally, we compare the proposed procedure with the existing method using a clinical trial data set. Journal: Journal of Nonparametric Statistics Pages: 59-70 Issue: 1 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.621024 File-URL: http://hdl.handle.net/10.1080/10485252.2011.621024 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:59-70 Template-Type: ReDIF-Article 1.0 Author-Name: Garth Tarr Author-X-Name-First: Garth Author-X-Name-Last: Tarr Author-Name: Samuel Müller Author-X-Name-First: Samuel Author-X-Name-Last: Müller Author-Name: Neville Weber Author-X-Name-First: Neville Author-X-Name-Last: Weber Title: A robust scale estimator based on pairwise means Abstract: We propose a new robust scale estimator, the pairwise mean scale estimator Pn, which in its most basic form is the interquartile range of the pairwise means. The use of pairwise means leads to a surprisingly high efficiency across many distributions of practical interest. The properties of Pn are presented under a unified generalised L-statistics framework, which encompasses numerous other scale estimators. Extensions to Pn are proposed, including taking the range of the middle τ×100% instead of just the middle 50% of the pairwise means as well as trimming and Winsorising both the original data and the pairwise means. Furthermore, we have implemented a method using adaptive trimming, which achieves a maximal breakdown value. We investigate the efficiency properties of the pairwise mean scale estimator relative to a number of other established robust scale estimators over a broad range of distributions using the corresponding maximum likelihood estimates as a common base for comparison. Journal: Journal of Nonparametric Statistics Pages: 187-199 Issue: 1 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.621424 File-URL: http://hdl.handle.net/10.1080/10485252.2011.621424 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:187-199 Template-Type: ReDIF-Article 1.0 Author-Name: Piet Groeneboom Author-X-Name-First: Piet Author-X-Name-Last: Groeneboom Author-Name: Geurt Jongbloed Author-X-Name-First: Geurt Author-X-Name-Last: Jongbloed Author-Name: Birgit Witte Author-X-Name-First: Birgit Author-X-Name-Last: Witte Title: A maximum smoothed likelihood estimator in the current status continuous mark model Abstract: We consider the problem of estimating the joint distribution function of the event time and a continuous mark variable based on censored data. More specifically, the event time is subject to current status censoring and the continuous mark is only observed in case inspection takes place after the event time. The nonparametric maximum likelihood estimator in this model is known to be inconsistent. We propose and study an alternative likelihood-based estimator, maximising a smoothed log-likelihood, hence called a maximum smoothed likelihood estimator (MSLE). This estimator is shown to be well defined and consistent, and a simple algorithm is described that can be used to compute it. The MSLE is compared with other estimators in a small simulation study. Journal: Journal of Nonparametric Statistics Pages: 85-101 Issue: 1 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.621952 File-URL: http://hdl.handle.net/10.1080/10485252.2011.621952 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:85-101 Template-Type: ReDIF-Article 1.0 Author-Name: Wangli Xu Author-X-Name-First: Wangli Author-X-Name-Last: Xu Author-Name: Xu Guo Author-X-Name-First: Xu Author-X-Name-Last: Guo Author-Name: Lixing Zhu Author-X-Name-First: Lixing Author-X-Name-Last: Zhu Title: Goodness-of-fitting for partial linear model with missing response at random Abstract: In this study, we consider the testing problem about the null hypothesis that the nonlinear part in the partial linear regression model with missing response at random is a parametric function or not against the alternative that it is nonparametric. By imputation and inverse probability weighting methods, we then construct two completed data sets. Two empirical process-based tests, from these completed data sets, are introduced. Under the null hypothesis and local alterative hypotheses, the limiting null distributions and power study of the test statistics are, respectively, investigated. A nonparametric Monte Carlo test procedure, which can automatically make the test procedure scale-invariant even when the test statistics are not scale-invariant, is applied to approximate the limiting null distributions of the test statistics. Simulation study is carried out to examine the performance of the tests. We illustrate the proposed method with a real data set on monozygotic twins. Journal: Journal of Nonparametric Statistics Pages: 103-118 Issue: 1 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.626410 File-URL: http://hdl.handle.net/10.1080/10485252.2011.626410 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:103-118 Template-Type: ReDIF-Article 1.0 Author-Name: Guo-Liang Fan Author-X-Name-First: Guo-Liang Author-X-Name-Last: Fan Author-Name: Han-Ying Liang Author-X-Name-First: Han-Ying Author-X-Name-Last: Liang Author-Name: Zhen-Sheng Huang Author-X-Name-First: Zhen-Sheng Author-X-Name-Last: Huang Title: Empirical likelihood for partially time-varying coefficient models with dependent observations Abstract: In this paper, we apply the empirical likelihood method to study the partially time-varying coefficient models with a random design and a fixed design under dependent assumptions. A nonparametric version of Wilks’ theorem is derived for the fixed-design case. For the random-design case, it is proved that the empirical log-likelihood ratio of the regression parameters admits a limiting distribution with a weighted sum of independent chi-squared distributions. In order that Wilks’ phenomenon holds, we propose an adjusted empirical log-likelihood (ADEL) ratio for the regression parameters. The ADEL is shown to have a standard chi-squared limiting distribution. Simulation studies are undertaken to indicate that the proposed methods work better than the normal approximation-based approach. Journal: Journal of Nonparametric Statistics Pages: 71-84 Issue: 1 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.626411 File-URL: http://hdl.handle.net/10.1080/10485252.2011.626411 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:71-84 Template-Type: ReDIF-Article 1.0 Author-Name: Aboubacar Amiri Author-X-Name-First: Aboubacar Author-X-Name-Last: Amiri Title: Recursive regression estimators with application to nonparametric prediction Abstract: In the case of dependent data, the purpose of this paper is to establish the exact asymptotic quadratic error of a parametric family of recursive kernel regression estimators. Based on this family of estimators, recursive nonparametric kernel predictors are studied. For mixing Markov processes, their almost sure convergence to the best predictor is established. Efficiency of these methods is also shown through numerical simulations highlighting their significantly reduced time of computation. Journal: Journal of Nonparametric Statistics Pages: 169-186 Issue: 1 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.626855 File-URL: http://hdl.handle.net/10.1080/10485252.2011.626855 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:169-186 Template-Type: ReDIF-Article 1.0 Author-Name: Rostyslav Maiboroda Author-X-Name-First: Rostyslav Author-X-Name-Last: Maiboroda Author-Name: Olena Sugakova Author-X-Name-First: Olena Author-X-Name-Last: Sugakova Title: Statistics of mixtures with varying concentrations with application to DNA microarray data analysis Abstract: A finite mixture model is considered in which the mixing probabilities vary from observation to observation. Estimation of mixture components distributions, functional moments and densities is discussed. Tests are proposed for testing hypotheses on the moments. An application to the analysis of DNA microarray data is considered. Journal: Journal of Nonparametric Statistics Pages: 201-215 Issue: 1 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.630076 File-URL: http://hdl.handle.net/10.1080/10485252.2011.630076 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:201-215 Template-Type: ReDIF-Article 1.0 Author-Name: Xiao-Feng Wang Author-X-Name-First: Xiao-Feng Author-X-Name-Last: Wang Author-Name: Deping Ye Author-X-Name-First: Deping Author-X-Name-Last: Ye Title: The effects of error magnitude and bandwidth selection for deconvolution with unknown error distribution Abstract: The error distribution is generally unknown in deconvolution problems with real applications. A separate independent experiment is thus often conducted to collect the additional noise data in these studies. In this paper, we study the nonparametric deconvolution estimation from a contaminated sample coupled with an additional noise sample. A ridge-based kernel deconvolution estimator is proposed and its asymptotic properties are investigated depending on the error magnitude. We then present a data-driven bandwidth selection algorithm by combining the bootstrap method and the idea of simulation extrapolation. The finite sample performance of the proposed methods and the effects of error magnitude are evaluated through simulation studies. A real data analysis for a gene Illumina BeadArray study is performed to illustrate the use of the proposed methods. Journal: Journal of Nonparametric Statistics Pages: 153-167 Issue: 1 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.647024 File-URL: http://hdl.handle.net/10.1080/10485252.2011.647024 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:153-167 Template-Type: ReDIF-Article 1.0 Author-Name: Suojin Wang Author-X-Name-First: Suojin Author-X-Name-Last: Wang Title: Editor's Report 2011 Journal: Journal of Nonparametric Statistics Pages: 1-1 Issue: 1 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.651897 File-URL: http://hdl.handle.net/10.1080/10485252.2012.651897 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:1-1 Template-Type: ReDIF-Article 1.0 Author-Name: Ji-Yeon Yang Author-X-Name-First: Ji-Yeon Author-X-Name-Last: Yang Author-Name: Jungmo Yoon Author-X-Name-First: Jungmo Author-X-Name-Last: Yoon Title: Construction of credible intervals for nonlinear regression models with unknown error distributions Abstract: There has been continuing interest in Bayesian regressions in which no parametric assumptions are imposed on the error distribution. In this study, we consider semiparametric Bayesian nonlinear regression models. We do not impose a parametric form for the likelihood function. Instead, we treat the true density function of error terms as an infinite-dimensional nuisance parameter and estimate it nonparametrically. Thereafter, we conduct a conventional parametric Bayesian inference using MCMC methods. We derive the asymptotic properties of the resulting estimator and identify conditions for adaptive estimation, under which our two-step Bayes estimator enjoys the same asymptotic efficiency as if we knew the true density. We compare the accuracy and coverage of the adaptive Bayesian point and interval estimators to those of the maximum likelihood estimator empirically, using simulated and real data. In particular, we observe that the Bayesian inference may be superior in numerical stability for small sample sizes. Journal: Journal of Nonparametric Statistics Pages: 813-848 Issue: 4 Volume: 31 Year: 2019 Month: 10 X-DOI: 10.1080/10485252.2019.1643865 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1643865 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:4:p:813-848 Template-Type: ReDIF-Article 1.0 Author-Name: Kangni Alemdjrodo Author-X-Name-First: Kangni Author-X-Name-Last: Alemdjrodo Author-Name: Yichuan Zhao Author-X-Name-First: Yichuan Author-X-Name-Last: Zhao Title: Reduce the computation in jackknife empirical likelihood for comparing two correlated Gini indices Abstract: The Gini index has been widely used as a measure of income (or wealth) inequality in social sciences. To construct a confidence interval for the difference of two Gini indices from the paired samples, Wang and Zhao [‘Jackknife Empirical Likelihood for Comparing Two Gini Indices’, The Canadian Journal of Statistics, 44(1), 102–119] used a profile jackknife empirical likelihood. However, the computing cost with the profile empirical likelihood could be very expensive. In this paper, we propose an alternative approach of the jackknife empirical likelihood method to reduce the computational cost. We also investigate the adjusted jackknife empirical likelihood and the bootstrap-calibrated jackknife empirical likelihood to improve coverage accuracy for small samples. Simulations show that the proposed methods perform better than Wang and Zhao's methods in terms of coverage accuracy and computational time. Real data applications demonstrate that the proposed methods work very well in practice. Journal: Journal of Nonparametric Statistics Pages: 849-866 Issue: 4 Volume: 31 Year: 2019 Month: 10 X-DOI: 10.1080/10485252.2019.1650925 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1650925 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:4:p:849-866 Template-Type: ReDIF-Article 1.0 Author-Name: Shengji Jia Author-X-Name-First: Shengji Author-X-Name-Last: Jia Author-Name: Chunming Zhang Author-X-Name-First: Chunming Author-X-Name-Last: Zhang Author-Name: Hulin Wu Author-X-Name-First: Hulin Author-X-Name-Last: Wu Title: Efficient semiparametric regression for longitudinal data with regularised estimation of error covariance function Abstract: Improving estimation efficiency for regression coefficients is an important issue in the analysis of longitudinal data, which involves estimating the covariance matrix of errors. But challenges arise in estimating the covariance matrix of longitudinal data collected at irregular or unbalanced time points. In this paper, we develop a regularisation method for estimating the covariance function and a stepwise procedure for estimating the parametric components efficiently in the varying-coefficient partially linear model. This procedure is also applicable to the varying-coefficient temporal mixed-effects model. Our method utilises the structure of the covariance function and thus has faster rates of convergence in estimating the covariance functions and outperforms the existing approaches in simulation studies. This procedure is easy to implement and its numerical performance is investigated using both simulated and real data. Journal: Journal of Nonparametric Statistics Pages: 867-886 Issue: 4 Volume: 31 Year: 2019 Month: 10 X-DOI: 10.1080/10485252.2019.1651853 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1651853 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:4:p:867-886 Template-Type: ReDIF-Article 1.0 Author-Name: Kwan-Young Bak Author-X-Name-First: Kwan-Young Author-X-Name-Last: Bak Author-Name: Jae-Hwan Jhong Author-X-Name-First: Jae-Hwan Author-X-Name-Last: Jhong Author-Name: Ja-Yong Koo Author-X-Name-First: Ja-Yong Author-X-Name-Last: Koo Title: Spatially adaptive binary classifier using B-splines and total variation penalty Abstract: This paper reports on our study of a binary classifier based on B-splines and the total variation penalty. The decision boundary of the proposed classifier is obtained using a variant of the hinge loss function. We restrict our focus to a two-dimensional predictor space to analyse the theoretical behaviour of the spline decision curve estimator. Theoretical investigation shows that the proposed estimator achieves the same optimal rate of convergence as in nonparametric regression estimation under some regularity conditions. The proposed method is implemented with a coordinate descent algorithm. Numerical studies using real and simulated data are conducted to complement the theoretical results. The results show that the proposed estimator adapts well to the data and yields more accurate predictions than other existing support vector machine methods. We also discuss directions for future research. Journal: Journal of Nonparametric Statistics Pages: 887-910 Issue: 4 Volume: 31 Year: 2019 Month: 10 X-DOI: 10.1080/10485252.2019.1663847 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1663847 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:4:p:887-910 Template-Type: ReDIF-Article 1.0 Author-Name: Jiwei Zhao Author-X-Name-First: Jiwei Author-X-Name-Last: Zhao Author-Name: Chi Chen Author-X-Name-First: Chi Author-X-Name-Last: Chen Title: Estimators based on unconventional likelihoods with nonignorable missing data and its application to a children's mental health study Abstract: Nonignorable missing data is common in studies where the outcome is relevant to the subject's behaviour. Ibrahim, Lipsitz, and Horton [(2001), ‘Using Auxiliary Data for Parameter Estimation with Non-ignorably Missing Outcomes’, Journal of the Royal Statistical Society: Series C (Applied Statistics), 50, 361–373] fitted a logistic regression for a binary outcome subject to nonignorable missing data, and they proposed to replace the outcome in the mechanism model with an auxiliary variable that is completely observed. They had to correctly specify a model for the auxiliary variable; unfortunately the outcome variable subject to nonignorable missingness is still involved. The correct specification of this model is mysterious. Instead, we propose two unconventional likelihood-based estimation procedures where the nonignorable missingness mechanism model could be completely bypassed. We apply our proposed methods to the children's mental health study and compare their performance with existing methods. The large sample properties of the proposed estimators are rigorously justified, and their finite sample behaviours are examined via comprehensive simulation studies. Journal: Journal of Nonparametric Statistics Pages: 911-931 Issue: 4 Volume: 31 Year: 2019 Month: 10 X-DOI: 10.1080/10485252.2019.1664739 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1664739 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:4:p:911-931 Template-Type: ReDIF-Article 1.0 Author-Name: Weiwei Wang Author-X-Name-First: Weiwei Author-X-Name-Last: Wang Author-Name: Xianyi Wu Author-X-Name-First: Xianyi Author-X-Name-Last: Wu Author-Name: Xiaobing Zhao Author-X-Name-First: Xiaobing Author-X-Name-Last: Zhao Author-Name: Xian Zhou Author-X-Name-First: Xian Author-X-Name-Last: Zhou Title: Quantile estimation of partially varying coefficient model for panel count data with informative observation times Abstract: Panel count data frequently arise in various applications such as medical research, social sciences and so on. In this paper, a partially varying coefficient model of the panel count data with informative observation times is developed to accommodate the nonlinear interact effects between covariates. For statistical inference of the unknown parameters, quantile regression approaches are proposed, in which the baseline function and the varying coefficients are approximated by B-spline functions. Moreover, asymptotic properties for the estimators are established. Some numerical studies are performed to confirm and evaluate the finite-sample behaviours of the proposed approaches. Finally, the proposed model is applied to the bladder cancer tumour data as an application. Journal: Journal of Nonparametric Statistics Pages: 932-951 Issue: 4 Volume: 31 Year: 2019 Month: 10 X-DOI: 10.1080/10485252.2019.1666128 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1666128 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:4:p:932-951 Template-Type: ReDIF-Article 1.0 Author-Name: Olivier Bouaziz Author-X-Name-First: Olivier Author-X-Name-Last: Bouaziz Author-Name: Elodie Brunel Author-X-Name-First: Elodie Author-X-Name-Last: Brunel Author-Name: Fabienne Comte Author-X-Name-First: Fabienne Author-X-Name-Last: Comte Title: Nonparametric survival function estimation for data subject to interval censoring case 2 Abstract: In this paper, we propose a new strategy of estimation for the survival function S, associated to a survival time subject to interval censoring case 2. Our method is based on a least squares contrast of regression type with parameters corresponding to the coefficients of the development of S on an orthonormal basis. We obtain a collection of projection estimators where the dimension of the projection space has to be adequately chosen via a model selection procedure. For compactly supported bases, we obtain adaptive results leading to general nonparametric rates. However, our results can be used for non-compactly supported bases, a true novelty in regression setting, and we use specifically the Laguerre basis which is ${\mathbb R}^+ $R+-supported and thus well suited when non-negative random variables are involved in the model. Simulation results comparing our proposal with previous strategies show that it works well in a very general context. A real dataset is considered to illustrate the methodology. Journal: Journal of Nonparametric Statistics Pages: 952-987 Issue: 4 Volume: 31 Year: 2019 Month: 10 X-DOI: 10.1080/10485252.2019.1669791 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1669791 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:4:p:952-987 Template-Type: ReDIF-Article 1.0 Author-Name: Patrick Marsh Author-X-Name-First: Patrick Author-X-Name-Last: Marsh Title: A two-sample nonparametric likelihood ratio test Abstract: This paper proposes a new test for the hypothesis that two samples have the same distribution. The likelihood ratio test of Portnoy [Portnoy, S. (1988), ‘Asymptotic Behaviour of Likelihood Methods for Exponential Families When the Number of Parameters Tends to Infinity’, Annals of Statistics, 16, 356–366] is applied in the context of the consistent series density estimator of Crain [Crain, B.R. (1974), ‘Estimation of Distributions Using Orthogonal Expansions’, Annals of Statistics, 2, 454–463] and Barron and Sheu [Barron, A.R., and Sheu, C.-H. (1991), ‘Approximation of Density Functions by Sequences of Exponential Families’. Annals of Statistics, 19, 1347–1369]. It is proven that the test, when suitably standardised, is asymptotically standard normal and consistent against any complementary fixed alternative. In comparison with established tests, such as the Kolmogorov–Smirnov, Cramér-von Mises and rank sum, median, and dispersion tests, the proposed tests enjoy broadly comparable finite sample size properties, but vastly superior power properties when considered over a range of different alternatives. Journal: Journal of Nonparametric Statistics Pages: 1053-1065 Issue: 8 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903486078 File-URL: http://hdl.handle.net/10.1080/10485250903486078 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:8:p:1053-1065 Template-Type: ReDIF-Article 1.0 Author-Name: Christian Genest Author-X-Name-First: Christian Author-X-Name-Last: Genest Author-Name: Johanna Nešlehová Author-X-Name-First: Johanna Author-X-Name-Last: Nešlehová Author-Name: Noomen Ben Ghorbal Author-X-Name-First: Noomen Author-X-Name-Last: Ben Ghorbal Title: Spearman's footrule and Gini's gamma: a review with complements Abstract: The scattered literature on Spearman's footrule and Gini's gamma is surveyed. The following topics are covered: finite-sample moments and asymptotic distribution under independence; large-sample distribution under arbitrary alternatives; asymptotic relative efficiency for testing independence; consistent asymptotic variance estimation through the jackknife; multivariate generalisations and uses. Complementary results and an extensive bibliography are provided, along with several original illustrations. Journal: Journal of Nonparametric Statistics Pages: 937-954 Issue: 8 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903499667 File-URL: http://hdl.handle.net/10.1080/10485250903499667 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:8:p:937-954 Template-Type: ReDIF-Article 1.0 Author-Name: Mohamed El Machkouri Author-X-Name-First: Mohamed Author-X-Name-Last: El Machkouri Author-Name: Radu Stoica Author-X-Name-First: Radu Author-X-Name-Last: Stoica Title: Asymptotic normality of kernel estimates in a regression model for random fields Abstract: We establish the asymptotic normality of the regression estimator in a fixed-design setting when the errors are given by a field of dependent random variables. The result applies to martingale-difference or strongly mixing random fields. On this basis, a statistical test that can be applied to image analysis is also presented. Journal: Journal of Nonparametric Statistics Pages: 955-971 Issue: 8 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903505893 File-URL: http://hdl.handle.net/10.1080/10485250903505893 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:8:p:955-971 Template-Type: ReDIF-Article 1.0 Author-Name: Dongliang Wang Author-X-Name-First: Dongliang Author-X-Name-Last: Wang Author-Name: Alan Hutson Author-X-Name-First: Alan Author-X-Name-Last: Hutson Author-Name: Daniel Gaile Author-X-Name-First: Daniel Author-X-Name-Last: Gaile Title: An exact bootstrap approach towards modification of the Harrell–Davis quantile function estimator for censored data Abstract: A new kernel quantile estimator is proposed for right-censored data, which takes the form of , where wj(u, c) is based on a beta kernel with bandwidth parameter c. The advantage of this estimator is that exact bootstrap methods may be employed to estimate the mean and variance of [Qcirc](u; c). It follows that a novel solution for finding the optimal bandwidth may be obtained through minimization of the exact bootstrap mean squared error (MSE) estimate of [Qcirc](u; c). We prove the large sample consistency of [Qcirc](u; c) for fixed values of c. A Monte Carlo simulation study shows that our estimator is significantly better than the product-limit quantile estimator [Qcirc]KM(u)=inf{t:[Fcirc]n(t)≥u}, with respect to various MSE criteria. For general simplicity, setting c=1 leads to an extension of classical Harrell–Davis estimator for censored data and performs well in simulations. The procedure is illustrated by an application to lung cancer survival data. Journal: Journal of Nonparametric Statistics Pages: 1039-1051 Issue: 8 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903524662 File-URL: http://hdl.handle.net/10.1080/10485250903524662 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:8:p:1039-1051 Template-Type: ReDIF-Article 1.0 Author-Name: Fadoua Balabdaoui Author-X-Name-First: Fadoua Author-X-Name-Last: Balabdaoui Author-Name: Kaspar Rufibach Author-X-Name-First: Kaspar Author-X-Name-Last: Rufibach Author-Name: Filippo Santambrogio Author-X-Name-First: Filippo Author-X-Name-Last: Santambrogio Title: Least-squares estimation of two-ordered monotone regression curves Abstract: In this paper, we consider the problem of finding the least-squares estimators of two isotonic regression curves and under the additional constraint that they are ordered, for example, . Given two sets of n data points y1, …, yn and z1, …, zn observed at (the same) design points, the estimates of the true curves are obtained by minimising the weighted least-squares criterion over the class of pairs of vectors (a, b)∈ℝn×ℝn such that a1≤a2≤···≤an, b1≤b2≤···≤bn, and ai≤bi, i=1, …, n. The characterisation of the estimators is established. To compute these estimators, we use an iterative projected subgradient algorithm, where the projection is performed with a ‘generalised’ pool-adjacent-violaters algorithm, a byproduct of this work. Then, we apply the estimation method to real data from mechanical engineering. Journal: Journal of Nonparametric Statistics Pages: 1019-1037 Issue: 8 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903548729 File-URL: http://hdl.handle.net/10.1080/10485250903548729 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:8:p:1019-1037 Template-Type: ReDIF-Article 1.0 Author-Name: Li Wang Author-X-Name-First: Li Author-X-Name-Last: Wang Author-Name: Lijian Yang Author-X-Name-First: Lijian Author-X-Name-Last: Yang Title: Simultaneous confidence bands for time-series prediction function Abstract: Although many types of confidence bands exist for nonparametric regression with i.i.d. data, theoretical properties of such bands have never been established under dependence. We propose simultaneous confidence bands for nonparametric prediction function of time-series data using spline estimation. Asymptotic properties are established under the assumption of strong mixing, and simulation experiments have provided strong evidence that corroborates with the asymptotic theory. As an application, after removing the environmental Kuznets curve trend effects, the impact of the economic intervention on environmental quality change is quantified for the USA and Japan, with different conclusions. Journal: Journal of Nonparametric Statistics Pages: 999-1018 Issue: 8 Volume: 22 Year: 2010 X-DOI: 10.1080/10485251003592575 File-URL: http://hdl.handle.net/10.1080/10485251003592575 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:8:p:999-1018 Template-Type: ReDIF-Article 1.0 Author-Name: Yogendra Chaubey Author-X-Name-First: Yogendra Author-X-Name-Last: Chaubey Author-Name: Naâmane Laïb Author-X-Name-First: Naâmane Author-X-Name-Last: Laïb Author-Name: Arusharka Sen Author-X-Name-First: Arusharka Author-X-Name-Last: Sen Title: Generalised kernel smoothing for non-negative stationary ergodic processes Abstract: In this paper, we consider a generalised kernel smoothing estimator of the regression function with non-negative support, using gamma probability densities as kernels, which are non-negative and have naturally varying shapes. It is based on a generalisation of Hille's lemma and a perturbation idea that allows us to deal with the problem at the boundary. Its uniform consistency and asymptotic normality are obtained at interior and boundary points, under a stationary ergodic process assumption, without using traditional mixing conditions. The asymptotic mean squared error of the estimator is derived and the optimal value of smoothing parameter is also discussed. Graphical illustrations of the proposed estimator are provided for simulated as well as for real data. A simulation study is also carried out to compare our method with the competing local linear method. Journal: Journal of Nonparametric Statistics Pages: 973-997 Issue: 8 Volume: 22 Year: 2010 X-DOI: 10.1080/10485251003605120 File-URL: http://hdl.handle.net/10.1080/10485251003605120 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:8:p:973-997 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: List of Reviewers Journal: Pages: 1067-1068 Issue: 8 Volume: 22 Year: 2010 X-DOI: 10.1080/10485252.2010.528689 File-URL: http://hdl.handle.net/10.1080/10485252.2010.528689 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:8:p:1067-1068 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Editorial Board Journal: Pages: ebi-ebi Issue: 8 Volume: 22 Year: 2010 X-DOI: 10.1080/10485252.2010.528691 File-URL: http://hdl.handle.net/10.1080/10485252.2010.528691 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:8:p:ebi-ebi Template-Type: ReDIF-Article 1.0 Author-Name: Dragan Radulović Author-X-Name-First: Dragan Author-X-Name-Last: Radulović Title: Necessary and sufficient conditions for the moving blocks bootstrap central limit theorem of the mean Abstract: For strictly stationary sequences Xi, we study the relations between statistics Zn=n−1/2∑ (Xi−EXi) and its Bootstrap counterpart We establish sufficient and necessary conditions for Central Limit Theorem in this setting and generalise the cases for which converges to Gaussian limit, while Zn fails to do so. In addition, we establish Bootstrap Central Limit Theorem without mixing conditions and identify the cases for which and Zn are asymptotically close, while both fail to converge in distribution. Journal: Journal of Nonparametric Statistics Pages: 343-357 Issue: 2 Volume: 24 Year: 2012 X-DOI: 10.1080/10485251003663517 File-URL: http://hdl.handle.net/10.1080/10485251003663517 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:343-357 Template-Type: ReDIF-Article 1.0 Author-Name: Wenzhuan Zhang Author-X-Name-First: Wenzhuan Author-X-Name-Last: Zhang Author-Name: Yingcun Xia Author-X-Name-First: Yingcun Author-X-Name-Last: Xia Title: Twicing local linear kernel regression smoothers Abstract: It is known that the local cubic smoother (LC) has a faster consistency rate than the popular local linear smoother (LL). However, LC often has a bigger mean squared error (MSE) than LL numerically for samples of finite size. By extending the idea of Stuetzle and Mittal [1979, ‘Some Comments on the Asymptotic Behavior of Robust Smoothers’, in Smoothing Techniques for Curve Estimation: Proceedings (chap. 11), eds. T. Gasser and M. Rosenbalatt, Berlin: Springer, pp. 191–195], we propose a new version of LC by ‘twicing’ the local linear smoother (TLL). Both asymptotic theory and finite sample simulations suggest that TLL has better efficiency than LL. Compared with LC, TLL has about the same asymptotic MSE (AMSE) as LC at the interior points and has a much smaller AMSE than LC at the boundary points. The TLL is also more stable than LC and has better performance than LC numerically. The application of TLL to estimate the first-order derivative of the regression function and other extensions are considered. Journal: Journal of Nonparametric Statistics Pages: 399-417 Issue: 2 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.636442 File-URL: http://hdl.handle.net/10.1080/10485252.2011.636442 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:399-417 Template-Type: ReDIF-Article 1.0 Author-Name: Guanqun Cao Author-X-Name-First: Guanqun Author-X-Name-Last: Cao Author-Name: Lijian Yang Author-X-Name-First: Lijian Author-X-Name-Last: Yang Author-Name: David Todem Author-X-Name-First: David Author-X-Name-Last: Todem Title: Simultaneous inference for the mean function based on dense functional data Abstract: A polynomial spline estimator is proposed for the mean function of dense functional data together with a simultaneous confidence band which is asymptotically correct. In addition, the spline estimator and its accompanying confidence band enjoy oracle efficiency in the sense that they are asymptotically the same as if all random trajectories are observed entirely and without errors. The confidence band is also extended to the difference of mean functions of two populations of functional data. Simulation experiments provide strong evidence that corroborates the asymptotic theory while computing is efficient. The confidence band procedure is illustrated by analysing the near-infrared spectroscopy data. Journal: Journal of Nonparametric Statistics Pages: 359-377 Issue: 2 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.638071 File-URL: http://hdl.handle.net/10.1080/10485252.2011.638071 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:359-377 Template-Type: ReDIF-Article 1.0 Author-Name: Zohra Guessoum Author-X-Name-First: Zohra Author-X-Name-Last: Guessoum Author-Name: Elias Ould Saïd Author-X-Name-First: Elias Author-X-Name-Last: Ould Saïd Title: Central limit theorem for the kernel estimator of the regression function for censored time series Abstract: In this paper, we consider the estimation of the regression function when the interest variable is subject to random censorship and the data satisfy some dependency conditions. We show that the new estimate [defined in Guessoum, Z., and Ould Saïd, E. (2008),‘On Nonparametric Estimation of the Regression Function Under Censorship Model’, Statistics & Decisions, 26, 159–177] suitably normalised is asymptotically normally distributed and the asymptotic variance is given explicitly. An application to confidence bands is given. Some simulations are drawn to lend further support to our theoretical results and to compare finite samples sizes with different rates of censoring and dependence. Journal: Journal of Nonparametric Statistics Pages: 379-397 Issue: 2 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.640678 File-URL: http://hdl.handle.net/10.1080/10485252.2011.640678 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:379-397 Template-Type: ReDIF-Article 1.0 Author-Name: Hoang-Long Ngo Author-X-Name-First: Hoang-Long Author-X-Name-Last: Ngo Title: An integrated cross-volatility estimation for asynchronous noisy data Abstract: Let σt be the instantaneous cross-volatility of two continuous semimartingales X and Y. In this paper, we introduce some estimators for the class of integrated cross-volatilities of the form where g is a continuous function and processes X and Y are sampled with microstructure noise and in an asynchronous way. In finance, it is widely accepted that the processes X and Y are reasonable models for the log return of price processes of stock and currency and our estimator is relevant in the context of intra-day high-frequency trading. Journal: Journal of Nonparametric Statistics Pages: 465-480 Issue: 2 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.647696 File-URL: http://hdl.handle.net/10.1080/10485252.2011.647696 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:465-480 Template-Type: ReDIF-Article 1.0 Author-Name: Anna Bargagliotti Author-X-Name-First: Anna Author-X-Name-Last: Bargagliotti Author-Name: Michael Orrison Author-X-Name-First: Michael Author-X-Name-Last: Orrison Title: Linear rank tests of uniformity: understanding inconsistent outcomes and the construction of new tests Abstract: Several nonparametric tests exist to test for differences among alternatives when using ranked data. Testing for differences among alternatives amounts to testing for uniformity over the set of possible permutations of the alternatives. Well-known tests of uniformity, such as the Friedman test or the Anderson test, are based on the impact of the usual limiting theorems (e.g. central limit theorem) and the results of different summary statistics (e.g. mean ranks, marginals, and pairwise ranks). Inconsistencies can occur among statistical tests’ outcomes – different statistical tests can yield different outcomes when applied to the same ranked data. In this paper, we describe a conceptual framework that naturally decomposes the underlying ranked data space. Using the framework, we explain why test results can differ and how their differences are related. In practice, one may choose a test based on the power or the structure of the ranked data. We discuss the implications of these choices and illustrate that for data meeting certain conditions, no existing test is effective in detecting nonuniformity. Finally, using a real data example, we illustrate how to construct new linear rank tests of uniformity. Journal: Journal of Nonparametric Statistics Pages: 481-495 Issue: 2 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.649282 File-URL: http://hdl.handle.net/10.1080/10485252.2011.649282 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:481-495 Template-Type: ReDIF-Article 1.0 Author-Name: Terence O'Neill Author-X-Name-First: Terence Author-X-Name-Last: O'Neill Author-Name: Steven Stern Author-X-Name-First: Steven Author-X-Name-Last: Stern Title: Finite population corrections for the Kolmogorov–Smirnov tests Abstract: In this paper, we examine the standard Kolmogorov–Smirnov test for assessing the goodness of fit for an assumed distribution, as well as the associated test of the equality of two distributions, in the case of a sample drawn without replacement from a finite population. In particular, we calculate an appropriate finite population adjustment factor for correcting the usual test statistics and numerically assess its properties. In addition, we provide an example of the use of the adjustment factor in sample size calculations which demonstrates the importance of incorporating the finite population effects in circumstances where the desired accuracy requires a very high sampling fraction. Journal: Journal of Nonparametric Statistics Pages: 497-504 Issue: 2 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2011.650169 File-URL: http://hdl.handle.net/10.1080/10485252.2011.650169 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:497-504 Template-Type: ReDIF-Article 1.0 Author-Name: Olimjon Sharipov Author-X-Name-First: Olimjon Author-X-Name-Last: Sharipov Author-Name: Martin Wendler Author-X-Name-First: Martin Author-X-Name-Last: Wendler Title: Bootstrap for the sample mean and for -statistics of mixing and near-epoch dependent processes Abstract: The validity of various bootstrapping methods has been proved for the sample mean of strongly mixing data. But in many applications, there appear nonlinear statistics of processes that are not strongly mixing. We investigate the nonoverlapping block bootstrap sequences which are near-epoch dependent on strong mixing or absolutely regular processes. This includes linear processes and conditional heteroskedastic processes as well as data from chaotic dynamical systems. We establish the strong consistency of the bootstrap distribution estimator not only for the sample mean, but also for U-statistics, which include such examples as Gini's mean difference or the χ2-test statistic. Journal: Journal of Nonparametric Statistics Pages: 317-342 Issue: 2 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.655274 File-URL: http://hdl.handle.net/10.1080/10485252.2012.655274 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:317-342 Template-Type: ReDIF-Article 1.0 Author-Name: Yang Xing Author-X-Name-First: Yang Author-X-Name-Last: Xing Author-Name: Bo Ranneby Author-X-Name-First: Bo Author-X-Name-Last: Ranneby Title: On strong Hellinger consistency of posterior distributions Abstract: We establish a sufficient condition ensuring strong Hellinger consistency of posterior distributions. We also prove a strong Hellinger consistency theorem for the pseudoposterior distributions based on the likelihood ratio with power 0<α<1, which are introduced by Walker and Hjort [2001 ‘On Bayesian Consistency’, J. R. Statist. Soc., B 63, 811–821]. Our result is an extension of their theorem for α=½. Journal: Journal of Nonparametric Statistics Pages: 505-515 Issue: 2 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.655275 File-URL: http://hdl.handle.net/10.1080/10485252.2012.655275 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:505-515 Template-Type: ReDIF-Article 1.0 Author-Name: Patrick Carmack Author-X-Name-First: Patrick Author-X-Name-Last: Carmack Author-Name: Jeffrey Spence Author-X-Name-First: Jeffrey Author-X-Name-Last: Spence Author-Name: William Schucany Author-X-Name-First: William Author-X-Name-Last: Schucany Title: Generalised correlated cross-validation Abstract: Since its introduction by [Stone, M. (1974), ‘Cross-validatory Choice and the Assessment of Statistical Predictions (with discussion)’, Journal of the Royal Statistical Society, B36, 111–133] and [Geisser, S. (1975), ‘The Predictive Sample Reuse Method with Applications’, Journal of the American Statistical Association, 70, 320–328], cross-validation has been studied and improved by several authors including [Burman, P., Chow, E., and Nolan, D. (1994), ‘A Cross-validatory Method for Dependent Data’, Biometrika, 81(2), 351–358], [Hart, J. and Yi, S. (1998), ‘One-sided Cross-validation’, Journal of the American Statistical Association, 93(442), 620–630], [Racine, J. (2000), ‘Consistent Cross-validatory Model-selection for Dependent Data: hv-block Cross-validation’, Journal of Econometrics, 99, 39–61], [Hart, J. and Lee, C. (2005), ‘Robustness of One-sided Cross-validation to Autocorrelation’, Journal of Multivariate Analysis, 92(1), 77–96], and [Carmack, P., Spence, J., Schucany, W., Gunst, R., Lin, Q., and Haley, R. (2009), ‘Far Casting Cross Validation’, Journal of Computational and Graphical Statistics, 18(4), 879–893]. Perhaps the most widely used and best known is generalised cross-validation (GCV) [Craven, P. and Wahba, G. (1979), ‘Smoothing Noisy Data with Spline Functions’, Numerical Mathematics, 31, 377–403], which establishes a single-pass method that penalises the fit by the trace of the smoother matrix assuming independent errors. We propose an extension to GCV in the context of correlated errors, which is motivated by a natural definition for residual degrees of freedom. The efficacy of the new method is investigated with a simulation experiment on a kernel smoother with bandwidth selection in local linear regression. Next, the winning methodology is illustrated by application to spatial modelling of fMRI data using a nonparametric semivariogram. We conclude with remarks about the heteroscedastic case and a potential maximum likelihood framework for Gaussian random processes. Journal: Journal of Nonparametric Statistics Pages: 269-282 Issue: 2 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.655733 File-URL: http://hdl.handle.net/10.1080/10485252.2012.655733 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:269-282 Template-Type: ReDIF-Article 1.0 Author-Name: N. Ushakov Author-X-Name-First: N. Author-X-Name-Last: Ushakov Author-Name: V. Ushakov Author-X-Name-First: V. Author-X-Name-Last: Ushakov Title: On bandwidth selection in kernel density estimation Abstract: In this paper, we suggest a new method of bandwidth selection in kernel density estimation. The new selector is less subject to the undersmoothing effect than the AMISE (asymptotic mean integrated square error) optimal bandwidth. Journal: Journal of Nonparametric Statistics Pages: 419-428 Issue: 2 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.655734 File-URL: http://hdl.handle.net/10.1080/10485252.2012.655734 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:419-428 Template-Type: ReDIF-Article 1.0 Author-Name: Constance van Eeden Author-X-Name-First: Constance Author-X-Name-Last: van Eeden Author-Name: James Zidek Author-X-Name-First: James Author-X-Name-Last: Zidek Title: Subset selection – extended Rizvi–Sobel for unequal sample sizes and its implementation Abstract: A nonparametric procedure is presented for selecting a subset of a set of k populations, containing the one with the largest (L) or smallest (S) αth quantile when independent samples are available from each and one population is the uniformly correct choice whatever be α. The result, an extension of a method previously proposed for the case of equal sample sizes, includes population i, if its αth sample quantile exceeds (in the case of L) the largest of the sample (α−β)th quantiles for the other populations, where 0<β<α. The selection index β is specified by the user. An obvious adaptation of this rule covers S. An asymptotic theory for the method gives a practical way of selecting β by optimising a linear combination of the probability of correct selection, which ideally should be large, and the expected subset size, which ideally should be small. Furthermore, the criterion provides a way of selecting the sample sizes in situations where the cost of obtaining the samples differs for the different populations. Journal: Journal of Nonparametric Statistics Pages: 299-315 Issue: 2 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.660482 File-URL: http://hdl.handle.net/10.1080/10485252.2012.660482 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:299-315 Template-Type: ReDIF-Article 1.0 Author-Name: Ying Dai Author-X-Name-First: Ying Author-X-Name-Last: Dai Author-Name: Shuangge Ma Author-X-Name-First: Shuangge Author-X-Name-Last: Ma Title: Variable selection for semiparametric regression models with iterated penalisation Abstract: Semiparametric regression models with multiple covariates are commonly encountered. When there are covariates that are not associated with a response variable, variable selection may lead to sparser models, more lucid interpretations and more accurate estimation. In this study, we adopt a sieve approach for the estimation of nonparametric covariate effects in semiparametric regression models. We adopt a two-step iterated penalisation approach for variable selection. In the first step, a mixture of Lasso and group Lasso penalties are employed to conduct the first-round variable selection and obtain the initial estimate. In the second step, a mixture of weighted Lasso and weighted group Lasso penalties, with weights constructed using the initial estimate, are employed for variable selection. We show that the proposed iterated approach has the variable selection consistency property, even when the number of unknown parameters diverges with sample size. Numerical studies, including simulation and analysis of a diabetes data set, show satisfactory performance of the proposed approach. Journal: Journal of Nonparametric Statistics Pages: 283-298 Issue: 2 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.661054 File-URL: http://hdl.handle.net/10.1080/10485252.2012.661054 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:283-298 Template-Type: ReDIF-Article 1.0 Author-Name: Guoyou Qin Author-X-Name-First: Guoyou Author-X-Name-Last: Qin Author-Name: Zhongyi Zhu Author-X-Name-First: Zhongyi Author-X-Name-Last: Zhu Author-Name: Wing Fung Author-X-Name-First: Wing Author-X-Name-Last: Fung Title: Robust estimation of the generalised partial linear model with missing covariates Abstract: In this paper, we propose robust estimation of the generalised partial linear model with covariates missing at random. The developed approach integrated the robust method and the method for dealing with missing data. Under some regularity conditions, we establish the asymptotic normality of the proposed estimator of the regression coefficients and show that the proposed estimator of the nonparametric function can achieve the optimal rate of convergence. It can be observed that the regression spline approach avoids some of the intricacies associated with the kernel method, and the robust estimation and inference can be carried out operationally as if a generalised linear model were used. Simulation studies are conducted to investigate the robustness of the proposed method. At the end, the proposed method is applied to a real data analysis for illustration. Journal: Journal of Nonparametric Statistics Pages: 517-530 Issue: 2 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.662972 File-URL: http://hdl.handle.net/10.1080/10485252.2012.662972 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:517-530 Template-Type: ReDIF-Article 1.0 Author-Name: Frédéric Ferraty Author-X-Name-First: Frédéric Author-X-Name-Last: Ferraty Author-Name: Nadia Kudraszow Author-X-Name-First: Nadia Author-X-Name-Last: Kudraszow Author-Name: Philippe Vieu Author-X-Name-First: Philippe Author-X-Name-Last: Vieu Title: Nonparametric estimation of a surrogate density function in infinite-dimensional spaces Abstract: A density function is generally not well defined in functional data context, but we can define a surrogate of a probability density, also called pseudo-density, when the small ball probability can be approximated by the product of two independent functions, one depending only on the centre of the ball. The aim of this paper is to study two kernel methods for estimating a surrogate probability density for functional data. We present asymptotic properties of these estimators: the convergence in probability and their rates. Simulations are given, including a functional version of smoother bootstrap selection of the parameters of the estimate. Journal: Journal of Nonparametric Statistics Pages: 447-464 Issue: 2 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.671943 File-URL: http://hdl.handle.net/10.1080/10485252.2012.671943 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:447-464 Template-Type: ReDIF-Article 1.0 Author-Name: Christophe Chesneau Author-X-Name-First: Christophe Author-X-Name-Last: Chesneau Author-Name: Isha Dewan Author-X-Name-First: Isha Author-X-Name-Last: Dewan Author-Name: Hassan Doosti Author-X-Name-First: Hassan Author-X-Name-Last: Doosti Title: Wavelet linear density estimation for associated stratified size-biased sample Abstract: Ramirez and Vidakovic [(2010), ‘Wavelet Density Estimation for Stratified Size-Biased Sample’, Journal of Statistical Planning and Inference, 140, 419–432] considered an estimator of the density function based on wavelets with independent stratified random variables from weighted distributions. They proved that it is L2-consistent. In this paper, we complete this result by determining the rate of convergence attained by a slightly modified version of their estimator (including an estimator of the normalisation parameters). Then, we explore the case when the random variables are negatively and positively associated within strata. The theory is illustrated with a simulation study. Journal: Journal of Nonparametric Statistics Pages: 429-445 Issue: 2 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.672024 File-URL: http://hdl.handle.net/10.1080/10485252.2012.672024 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:429-445 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: 2011 Best Paper Award Journal: Journal of Nonparametric Statistics Pages: 267-267 Issue: 2 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.674774 File-URL: http://hdl.handle.net/10.1080/10485252.2012.674774 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:267-267 Template-Type: ReDIF-Article 1.0 Author-Name: Mark Fey Author-X-Name-First: Mark Author-X-Name-Last: Fey Author-Name: Kevin Clarke Author-X-Name-First: Kevin Author-X-Name-Last: Clarke Title: Consistency of choice in nonparametric multiple comparisons Abstract: In this paper, we are interested in the inconsistencies that can arise in the context of rank-based multiple comparisons. It is well known that these inconsistencies exist, but we prove that every possible distribution-free rank-based multiple comparison procedure with certain reasonable properties is susceptible to these phenomena. The proof is based on a generalisation of Arrow's theorem, a fundamental result in social choice theory which states that when faced with three or more alternatives, it is impossible to rationally aggregate preference rankings subject to certain desirable properties. Applying this theorem to treatment rankings, we generalise a number of existing results in the literature and demonstrate that procedures that use rank sums cannot be improved. Finally, we show that the best possible procedures are based on the Friedman rank statistic and the k-sample sign statistic, in that these statistics minimise the potential for paradoxical results. Journal: Journal of Nonparametric Statistics Pages: 531-541 Issue: 2 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.675436 File-URL: http://hdl.handle.net/10.1080/10485252.2012.675436 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:2:p:531-541 Template-Type: ReDIF-Article 1.0 Author-Name: Wojciech Maciak Author-X-Name-First: Wojciech Author-X-Name-Last: Maciak Title: Exact null distribution for ≤25 and probability approximations for Spearman's score in an absence of ties Abstract: Spearman's rank correlation test is a widely used statistical method for testing the correlation between two samples. Unfortunately, the evaluation of the exact distribution of this statistic is difficult and approximation obtained by using the normal distribution is not accurate for moderate sample sizes. In this paper, the critical values for samples 11≤n≤25 are provided. On the basis of the calculated exact values, the accuracy of different approximation methods is discussed. The use of approximation obtained by using the Edgeworth series is recommended in cases when the exact distribution is not available. Journal: Journal of Nonparametric Statistics Pages: 113-133 Issue: 1 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802401038 File-URL: http://hdl.handle.net/10.1080/10485250802401038 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:1:p:113-133 Template-Type: ReDIF-Article 1.0 Author-Name: André Mas Author-X-Name-First: André Author-X-Name-Last: Mas Author-Name: Besnik Pumo Author-X-Name-First: Besnik Author-X-Name-Last: Pumo Title: Functional linear regression with derivatives Abstract: We introduce a new model of linear regression for random functional inputs taking into account the first-order derivative of the data. We propose an estimation method that comes down to solving a special linear inverse problem. Our procedure tackles the problem through a double and synchronised penalisation. An asymptotic expansion of the mean square prevision error is given. The model and the method are applied to a benchmark dataset of spectrometric curves and compared with other functional models. Journal: Journal of Nonparametric Statistics Pages: 19-40 Issue: 1 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802401046 File-URL: http://hdl.handle.net/10.1080/10485250802401046 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:1:p:19-40 Template-Type: ReDIF-Article 1.0 Author-Name: Xin Dang Author-X-Name-First: Xin Author-X-Name-Last: Dang Author-Name: Robert Serfling Author-X-Name-First: Robert Author-X-Name-Last: Serfling Author-Name: Weihua Zhou Author-X-Name-First: Weihua Author-X-Name-Last: Zhou Title: Influence functions of some depth functions, and application to depth-weighted L-statistics Abstract: Depth functions are increasingly being used in building nonparametric outlier detectors and in constructing useful nonparametric statistics such as depth-weighted L-statistics (DL-statistics). Robustness of a depth function is an essential property for such applications. Here, robustness of three key depth functions, spatial, simplicial, and generalised Tukey, is explored via the influence function (IF) approach. For all three depths, the IFs are derived and found to be bounded, an important robustness property, and are applied to evaluate two other robustness features, gross error sensitivity and local shift sensitivity. These IFs are also used as components of the IFs of associated DL-statistics, for which through a standard approach consistency and asymptotic normality are then derived. In turn, the asymptotic normality is applied to obtain asymptotic relative efficiencies (ARE). For spatial depth, two forms of weight function suggested in the recent literature are considered and AREs in comparison with the mean are obtained. For all three depths and one of these weight functions, finite sample REs are obtained by simulation under normal, contaminated normal, and heavy-tailed t distributions. As a technical tool of general interest, needed here with the simplicial depth, the IF of a general U-statistic is derived. Journal: Journal of Nonparametric Statistics Pages: 49-66 Issue: 1 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802447981 File-URL: http://hdl.handle.net/10.1080/10485250802447981 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:1:p:49-66 Template-Type: ReDIF-Article 1.0 Author-Name: J. Campbell Author-X-Name-First: J. Author-X-Name-Last: Campbell Title: Singularity estimation via structural intensity: applications and modifications Abstract: The problem of determining the number and location of singularities in a nonparametric setting is of significant practical and theoretical importance. In this paper, we examine an interesting new technique, the so-called strucural intensity of the wavelet modulus maxima that was recently suggested by Bigot [J. Bigot, A scale-space approach with wavelets to singularity estimation, ESAIM Probab. Statist. 9 (2005), pp. 143–164 (electronic)]. In doing so, an upper bound on the asymptotic rate of convergence for the associated estimator is determined and appropriate modifications are suggested where the empirical estimation technique is found to be inappropriate or otherwise simply left undefined. These clarifications should enable this promising tool to be employed with more confidence in future applications. Journal: Journal of Nonparametric Statistics Pages: 67-84 Issue: 1 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802449755 File-URL: http://hdl.handle.net/10.1080/10485250802449755 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:1:p:67-84 Template-Type: ReDIF-Article 1.0 Author-Name: Paul Janssen Author-X-Name-First: Paul Author-X-Name-Last: Janssen Author-Name: Jan Swanepoel Author-X-Name-First: Jan Author-X-Name-Last: Swanepoel Author-Name: Noël Veraverbeke Author-X-Name-First: Noël Author-X-Name-Last: Veraverbeke Title: New tests for exponentiality against new better than used in th quantile Abstract: A new characterisation of the exponential distribution in a wide class of new better than used in pth quantile (NBUp) lifetime distributions is presented. This leads to new classes of scale-free goodness-of-fit tests for exponentiality against NBUp alternatives. The limiting distributions of the test statistics under the null and alternative hypotheses are derived and the tests are shown to be consistent against NBUp alternatives. Pitman efficacies are calculated and a limited Monte Carlo study is conducted to compare the tests with regard to power for small and moderate sample sizes against a range of alternative distributions. On the basis of overall good performance and ease of computation, a member of the class of test statistics which is based on the sample Winsorised mean is recommended as a scale-free goodness-of-fit test for the exponential distribution. Journal: Journal of Nonparametric Statistics Pages: 85-97 Issue: 1 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802454953 File-URL: http://hdl.handle.net/10.1080/10485250802454953 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:1:p:85-97 Template-Type: ReDIF-Article 1.0 Author-Name: Xiangning Huang Author-X-Name-First: Xiangning Author-X-Name-Last: Huang Author-Name: Baibing Li Author-X-Name-First: Baibing Author-X-Name-Last: Li Title: Dichotomous transformations for statistical inference about odds ratios Abstract: Dichotomous transformations for continuous outcomes are commonly used. In this paper, we investigate dichotomisation for statistical inference about odds ratios in a situation where two underlying distributions from which independent samples are drawn are skewed and unknown. Under some mild conditions it is shown that a suitable choice of the cutpoint of a dichotomous transformation must lie within the range bounded by the two medians of the two underlying distributions, within which there exists a unique optimal cutpoint in terms of the asymptotic efficiency of point estimation and hypothesis testing. The issue of selecting a cutpoint is also linked to the choice amongst some existing non-parametric tests. Journal: Journal of Nonparametric Statistics Pages: 41-48 Issue: 1 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802471551 File-URL: http://hdl.handle.net/10.1080/10485250802471551 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:1:p:41-48 Template-Type: ReDIF-Article 1.0 Author-Name: Gopaldeb Chattopadhyay Author-X-Name-First: Gopaldeb Author-X-Name-Last: Chattopadhyay Title: On a class of two-sample partially sequential nonparametric tests for bivariate ordinal data under restricted alternatives Abstract: In 1977, Wolfe introduced a partially sequential scheme to capitalise the best aspects of both fixed and sequential design. This scheme is instrumental in reducing time and/or cost of the experiment when one sample is very difficult to obtain and/or costly compared with the other one. However, Wolfe's scheme is for continuous data. Chattopadhyay extended this idea of partially sequential technique for univariate ordinal data in 2002. However, in real life, bivariate ordinal data are quite common. The present article is an extension of Chattopadhyay's work for bivariate ordinal data. Like previously, in this article we also build a suitable stopping rule based on a fixed number of observations drawn from the first population and draw sequentially a random number of observations from the second population, using that stopping rule. We now suggest two types of test statistics, and their various asymptotic properties are explored. An extensive simulation study is also given that compares the performance of the two types of proposed test statistics. Journal: Journal of Nonparametric Statistics Pages: 99-111 Issue: 1 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802496731 File-URL: http://hdl.handle.net/10.1080/10485250802496731 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:1:p:99-111 Template-Type: ReDIF-Article 1.0 Author-Name: L. Galtchouk Author-X-Name-First: L. Author-X-Name-Last: Galtchouk Author-Name: S. Pergamenshchikov Author-X-Name-First: S. Author-X-Name-Last: Pergamenshchikov Title: Sharp non-asymptotic oracle inequalities for non-parametric heteroscedastic regression models Abstract: An adaptive non-parametric estimation procedure is constructed for heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound for a quadratic risk (oracle inequality) is obtained. Journal: Journal of Nonparametric Statistics Pages: 1-18 Issue: 1 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802504096 File-URL: http://hdl.handle.net/10.1080/10485250802504096 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:1:p:1-18 Template-Type: ReDIF-Article 1.0 Author-Name: Natalie Neumeyer Author-X-Name-First: Natalie Author-X-Name-Last: Neumeyer Title: A bootstrap version of the residual-based smooth empirical distribution function Abstract: In this paper, we consider estimating the error distribution in a non-parametric regression model by a smooth version of the empirical distribution function of residuals. We show that a classical residual bootstrap version of the resulting residual-based empirical process joins the same limiting distribution. From this result, consistency of various goodness-of-fit tests in non-parametric regression models is obtained. Journal: Journal of Nonparametric Statistics Pages: 153-174 Issue: 2 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250801908363 File-URL: http://hdl.handle.net/10.1080/10485250801908363 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:2:p:153-174 Template-Type: ReDIF-Article 1.0 Author-Name: R.J. Karunamuni Author-X-Name-First: R.J. Author-X-Name-Last: Karunamuni Author-Name: T. Liang Author-X-Name-First: T. Author-X-Name-Last: Liang Author-Name: J. Wu Author-X-Name-First: J. Author-X-Name-Last: Wu Title: Robust empirical Bayes tests for discrete distributions Abstract: In this paper, we investigate the empirical Bayes (EB) linear loss two-action problem for discrete distributions. Rates of convergence of the excess risk (the regret) of the EB rules are the main interest here. Previous results on the same problem have examined EB rules in the discrete exponential family or in particular types of discrete distributions. Here, we study EB rules under very general set-up, where the distributions of the observations are not fixed. When specialised to specific distributions, however, our results reduce to similar results available in the literature for such specific distributions. We show that the rates of convergence of the proposed EB rules are of the exponential order of the form O(exp(−cdn)), where {dn} is a sequence of positive numbers decreasing to zero as n→∞, with n being the number of observations. Another distinct feature of our results is that they are stated for a class of EB rules for the present problem, whereas some particular EB rules have been studied in previous work. Journal: Journal of Nonparametric Statistics Pages: 101-113 Issue: 2 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250801908371 File-URL: http://hdl.handle.net/10.1080/10485250801908371 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:2:p:101-113 Template-Type: ReDIF-Article 1.0 Author-Name: Sidi Maouloud Author-X-Name-First: Sidi Author-X-Name-Last: Maouloud Title: Some uniform large deviation results in nonparametric function estimation Abstract: In this paper, we investigate large deviation asymptotics involving classes of nonparametric estimates. We introduce a random process, say Zn, which allows to derive, using the contraction principle, results for several nonparametric estimates from the large deviations principle stated for Zn. The usual examples of nonparametric estimates include the histogram density estimate as well as the regressogram. Note that uniform behaviours over classes of density and regression functions as well as over classes of their estimates have been considered. Journal: Journal of Nonparametric Statistics Pages: 129-152 Issue: 2 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250801908389 File-URL: http://hdl.handle.net/10.1080/10485250801908389 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:2:p:129-152 Template-Type: ReDIF-Article 1.0 Author-Name: Hanxiang Peng Author-X-Name-First: Hanxiang Author-X-Name-Last: Peng Title: Efficient inference in a semiparametric generalised linear model Abstract: In this article, we calculate an explicit formula of the efficient influence function of the regression parameter in a semiparametric generalised linear model using the method of orthogonality calculations. We construct an efficient estimate of the parameter of interest. Journal: Journal of Nonparametric Statistics Pages: 115-127 Issue: 2 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250801920913 File-URL: http://hdl.handle.net/10.1080/10485250801920913 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:2:p:115-127 Template-Type: ReDIF-Article 1.0 Author-Name: Jiexiang Li Author-X-Name-First: Jiexiang Author-X-Name-Last: Li Title: Asymptotic distribution of local medians Abstract: The estimation of the regression function r(x)=E[Y|X=x] is very important because of its wide applications. Local median estimators with fixed bandwidth and random bandwidth are established and investigated. The limiting distribution of the estimators proposed in the paper is shown to be normal. The random fields are assumed to satisfy general mixing conditions. Journal: Journal of Nonparametric Statistics Pages: 175-185 Issue: 2 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250801948286 File-URL: http://hdl.handle.net/10.1080/10485250801948286 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:2:p:175-185 Template-Type: ReDIF-Article 1.0 Author-Name: F. Ferraty Author-X-Name-First: F. Author-X-Name-Last: Ferraty Author-Name: P. Vieu Author-X-Name-First: P. Author-X-Name-Last: Vieu Title: Erratum of: ‘Non-parametric models for functional data, with application in regression, time-series prediction and curve discrimination’ Abstract: A topological hypothesis was omitted during the statement of the results in [P. Ferraty and P. Vieu, Nonparametric models for functional data, with application in regression, time-series prediction and curve discrimination, Nonparamet. Statist. 16 (2004), pp. 111–125]. This erratum states this additional hypothesis. It also provides a wide class of examples of functional spaces of statistical interest for which this new hypothesis is satisfied. Journal: Journal of Nonparametric Statistics Pages: 187-189 Issue: 2 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250801999453 File-URL: http://hdl.handle.net/10.1080/10485250801999453 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:2:p:187-189 Template-Type: ReDIF-Article 1.0 Author-Name: Raymond Carroll Author-X-Name-First: Raymond Author-X-Name-Last: Carroll Author-Name: Xiaohong Chen Author-X-Name-First: Xiaohong Author-X-Name-Last: Chen Author-Name: Yingyao Hu Author-X-Name-First: Yingyao Author-X-Name-Last: Hu Title: Identification and estimation of nonlinear models using two samples with nonclassical measurement errors Abstract: This paper considers identification and estimation of a general nonlinear errors-in-variables (EIV) model using two samples. Both samples consist of a dependent variable, some error-free covariates, and an error-prone covariate, for which the measurement error has unknown distribution and could be arbitrarily correlated with the latent true values, and neither sample contains an accurate measurement of the corresponding true variable. We assume that the regression model of interest – the conditional distribution of the dependent variable given the latent true covariate and the error-free covariates – is the same in both samples, but the distributions of the latent true covariates vary with observed error-free discrete covariates. We first show that the general latent nonlinear model is nonparametrically identified using the two samples when both could have nonclassical errors, without either instrumental variables or independence between the two samples. When the two samples are independent and the nonlinear regression model is parameterised, we propose sieve quasi maximum likelihood estimation (Q-MLE) for the parameter of interest, and establish its root-n consistency and asymptotic normality under possible misspecification, and its semiparametric efficiency under correct specification, with easily estimated standard errors. A Monte Carlo simulation and a data application are presented to show the power of the approach. Journal: Journal of Nonparametric Statistics Pages: 379-399 Issue: 4 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250902874688 File-URL: http://hdl.handle.net/10.1080/10485250902874688 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:4:p:379-399 Template-Type: ReDIF-Article 1.0 Author-Name: Dmitrij Celov Author-X-Name-First: Dmitrij Author-X-Name-Last: Celov Author-Name: Remigijus Leipus Author-X-Name-First: Remigijus Author-X-Name-Last: Leipus Author-Name: Anne Philippe Author-X-Name-First: Anne Author-X-Name-Last: Philippe Title: Asymptotic normality of the mixture density estimator in a disaggregation scheme Abstract: The paper concerns the asymptotic distribution of the mixture density estimator, proposed by Leipus et al. [Leipus, R., Oppenheim, G., Philippe, A., and Viano, M.-C. (2006), ‘Orthogonal Series Density Estimation in a Disaggregation Scheme’, Journal of Statistical Planning and Inference, 136, 2547–2571], in the aggregation/disaggregation problem of random parameter AR(1) process. We prove that, under mild conditions on the (semiparametric) form of the mixture density, the estimator is asymptotically normal. The proof is based on the limit theory for the quadratic form in linear random variables developed by Bhansali et al. [Bhansali, R.J., Giraitis, L., and Kokoszka, P.S. (2007), Approximations and Limit Theory for Quadratic Forms of Linear Processes’, Stochastic Processes and their Applications, 117, 71–95]. The moving average representation of the aggregated process is investigated. A simulation study illustrates the result. Journal: Journal of Nonparametric Statistics Pages: 425-442 Issue: 4 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903045528 File-URL: http://hdl.handle.net/10.1080/10485250903045528 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:4:p:425-442 Template-Type: ReDIF-Article 1.0 Author-Name: Aurore Delaigle Author-X-Name-First: Aurore Author-X-Name-Last: Delaigle Author-Name: Peter Hall Author-X-Name-First: Peter Author-X-Name-Last: Hall Title: Discussion of ‘identification and estimation of non-linear models using two samples with nonclassical measurement errors’ Abstract: We would like to congratulate the authors for solving a complex, novel and stimulating problem of identification and estimation in a measurement error context. We also thank the Executive Editor for giving us the opportunity to discuss this work. Our main contribution to this discussion will be to try to develop the necessary insight into the methodology and its properties, with the aim of allowing other readers to better appreciate their highly original approach. We also raise a few points that the authors may wish to develop. Journal: Journal of Nonparametric Statistics Pages: 401-404 Issue: 4 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903105017 File-URL: http://hdl.handle.net/10.1080/10485250903105017 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:4:p:401-404 Template-Type: ReDIF-Article 1.0 Author-Name: Young Truong Author-X-Name-First: Young Author-X-Name-Last: Truong Title: Discussion of ‘identification and estimation of nonlinear models using two samples with nonclassical measurement Errors’ by Carroll et al. Abstract: Carroll et al. described a very general framework for problems involving measurement errors. The approach was based on the sieve likelihood principle where the dimension of the parameter space is allowed to grow with sample size. Thus the procedure includes many well-known estimators as special cases. In this discussion, a specific class of estimators based on B-splines will be described. It is observed that certain regularity conditions will be required to ensure the existence of the maximum likelihood estimators. Journal: Journal of Nonparametric Statistics Pages: 415-418 Issue: 4 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903181083 File-URL: http://hdl.handle.net/10.1080/10485250903181083 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:4:p:415-418 Template-Type: ReDIF-Article 1.0 Author-Name: Marie-Luce Taupin Author-X-Name-First: Marie-Luce Author-X-Name-Last: Taupin Title: Comment on identification and estimation of nonlinear models using two samples with nonclassical measurement errors Abstract: A major challenge in statistics is to make inferences in the presence of measurement error or mismeasurement variables. Such mismeasurements appear in various contexts such as econometrics, biology or medicine. The paper by Carroll, Chen and Hu is completely in line with this challenging task. In this context, I would like to express my sincere and great appreciation for their contribution to this topic. It is a great pleasure for me to have the opportunity to contribute a discussion of this paper. Journal: Journal of Nonparametric Statistics Pages: 409-414 Issue: 4 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903197212 File-URL: http://hdl.handle.net/10.1080/10485250903197212 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:4:p:409-414 Template-Type: ReDIF-Article 1.0 Author-Name: Nader Gemayel Author-X-Name-First: Nader Author-X-Name-Last: Gemayel Author-Name: Elizabeth Stasny Author-X-Name-First: Elizabeth Author-X-Name-Last: Stasny Author-Name: Douglas Wolfe Author-X-Name-First: Douglas Author-X-Name-Last: Wolfe Title: Optimal ranked set sampling estimation based on medians from multiple set sizes Abstract: Ranked set sampling (RSS) is a sample selection technique that makes use of expert knowledge to rank sample units before measuring them. Even though rankings are not always perfect, RSS is useful in situations where obtaining measurements is costly, difficult, or destructive. Research in this area has tended to focus on the case where all set sizes are equal. This article represents a departure from that setting because we encounter different set sizes within a single sample. More specifically, we propose an alternative estimator for the median of a symmetric distribution using medians of ranked set samples of various set sizes from such a distribution. This estimator is seen to be robust over a wide class of symmetric distributions. Journal: Journal of Nonparametric Statistics Pages: 517-527 Issue: 4 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903301517 File-URL: http://hdl.handle.net/10.1080/10485250903301517 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:4:p:517-527 Template-Type: ReDIF-Article 1.0 Author-Name: Alexandre Leblanc Author-X-Name-First: Alexandre Author-X-Name-Last: Leblanc Title: A bias-reduced approach to density estimation using Bernstein polynomials Abstract: Mixtures of Beta densities have led to different methods of density estimation for univariate data assumed to have compact support. One such method relies on Bernstein polynomials and leads to good approximation properties for the resulting estimator of the underlying density f. In particular, if f is twice continuously differentiable, this estimator can be shown to attain the optimal nonparametric convergence rate of n−4/5 in terms of mean integrated squared error (MISE). However, this rate cannot be improved upon directly when relying on the usual Bernstein polynomials, no matter what other assumptions are made on the smoothness of f.In this note, we show how a simple method of bias reduction can lead to a Bernstein-based estimator that does achieve a higher rate of convergence. Precisely, we exhibit a bias-corrected estimator that achieves the optimal nonparametric MISE rate of n−8/9 when the underlying density f is four times continuously differentiable on its support. Journal: Journal of Nonparametric Statistics Pages: 459-475 Issue: 4 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903318107 File-URL: http://hdl.handle.net/10.1080/10485250903318107 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:4:p:459-475 Template-Type: ReDIF-Article 1.0 Author-Name: Serge Guillas Author-X-Name-First: Serge Author-X-Name-Last: Guillas Author-Name: Ming-Jun Lai Author-X-Name-First: Ming-Jun Author-X-Name-Last: Lai Title: Bivariate splines for spatial functional regression models Abstract: We consider the functional linear regression model where the explanatory variable is a random surface and the response is a real random variable, in various situations where both the explanatory variable and the noise can be unbounded and dependent. Bivariate splines over triangulations represent the random surfaces. We use this representation to construct least squares estimators of the regression function with a penalisation term. Under the assumptions that the regressors in the sample span a large enough space of functions, bivariate splines approximation properties yield the consistency of the estimators. Simulations demonstrate the quality of the asymptotic properties on a realistic domain. We also carry out an application to ozone concentration forecasting over the USA that illustrates the predictive skills of the method. Journal: Journal of Nonparametric Statistics Pages: 477-497 Issue: 4 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903323180 File-URL: http://hdl.handle.net/10.1080/10485250903323180 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:4:p:477-497 Template-Type: ReDIF-Article 1.0 Author-Name: Han Hong Author-X-Name-First: Han Author-X-Name-Last: Hong Title: Comment for identification and estimation of nonlinear models using two samples with nonclassical measurement errors, by Carroll, Chen and Hu Abstract: This is a very interesting paper that develops nonparametric identification results and and semiparametric estimators for a nonparametric and semiparametric nonclassical measurement error model using a combination of a primary data set and an auxiliary data set. Their estimator not only achieves the semiparametric efficiency bound when the conditional regression model is correctly specified parametrically, but also performs well in finite sample simulation designs. In their paper, an application of their method to studying the relation between the amount of beta-carotene from food and the latent true daily long-term intake of beta-carotene using two data sets from the Eating at America's Table Study (EATS) and the Observing Protein and Energy Nutrition study shows that ignoring measurement errors in the EATS data set leads to substantial attenuation bias in the regression coefficient. Journal: Journal of Nonparametric Statistics Pages: 405-408 Issue: 4 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903329542 File-URL: http://hdl.handle.net/10.1080/10485250903329542 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:4:p:405-408 Template-Type: ReDIF-Article 1.0 Author-Name: Lan Xue Author-X-Name-First: Lan Author-X-Name-Last: Xue Author-Name: Jing Wang Author-X-Name-First: Jing Author-X-Name-Last: Wang Title: Distribution function estimation by constrained polynomial spline regression Abstract: A smooth monotone polynomial spline (PS) estimator is proposed for the cumulative distribution function. The proposed method applies a constrained PS regression to smooth the empirical distribution function, while simultaneously ensures monotonicity by imposing a set of linear constraints on the coefficients of the PS functions. This feature is not shared by its kernel counterpart in [Cheng, M.Y., and Peng, L. (2002), ‘Regression Modeling for Nonparametric Estimation of Distribution and Quantile Functions’, Statistica Sinica, 12, 1043–1060], as the kernel estimator is not necessarily monotone. Under mild assumptions, both L2 and uniform convergence rates are obtained. Our simulation studies show that the proposed estimator has better finite sample performance than the simple empirical distribution function. We also illustrate the use of the proposed method by analysing two real data examples. Journal: Journal of Nonparametric Statistics Pages: 443-457 Issue: 4 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903336802 File-URL: http://hdl.handle.net/10.1080/10485250903336802 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:4:p:443-457 Template-Type: ReDIF-Article 1.0 Author-Name: Xiao Song Author-X-Name-First: Xiao Author-X-Name-Last: Song Author-Name: Shuangge Ma Author-X-Name-First: Shuangge Author-X-Name-Last: Ma Title: Penalised variable selection with U-estimates Abstract: U-estimates are defined as maximisers of objective functions that are U-statistics. As an alternative to M-estimates, U-estimates have been extensively used in linear regression, classification, survival analysis, and many other areas. They may rely on weaker data and model assumptions and be preferred over alternatives. In this article, we investigate penalised variable selection with U-estimates. We propose smooth approximations of the objective functions, which can greatly reduce computational cost without affecting asymptotic properties. We study penalised variable selection using penalties that have been well investigated with M-estimates, including the LASSO, adaptive LASSO, and bridge, and establish their asymptotic properties. Generically applicable computational algorithms are described. Performance of the penalised U-estimates is assessed using numerical studies. Journal: Journal of Nonparametric Statistics Pages: 499-515 Issue: 4 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903348781 File-URL: http://hdl.handle.net/10.1080/10485250903348781 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:4:p:499-515 Template-Type: ReDIF-Article 1.0 Author-Name: Yury Kutoyants Author-X-Name-First: Yury Author-X-Name-Last: Kutoyants Title: On the goodness-of-fit testing for ergodic diffusion processes Abstract: We consider the goodness-of-fit testing problem for ergodic diffusion processes. The basic hypothesis is supposed to be simple. The diffusion coefficient is known and the alternatives are described by the different trend coefficients. We study the asymptotic distribution of the Cramér–von Mises type tests based on the empirical distribution function and local time estimator of the invariant density. Particularly, we propose a transformation which makes these tests asymptotically distribution-free. Journal: Journal of Nonparametric Statistics Pages: 529-543 Issue: 4 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903359564 File-URL: http://hdl.handle.net/10.1080/10485250903359564 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:4:p:529-543 Template-Type: ReDIF-Article 1.0 Author-Name: Raymond Carroll Author-X-Name-First: Raymond Author-X-Name-Last: Carroll Author-Name: Xiaohong Chen Author-X-Name-First: Xiaohong Author-X-Name-Last: Chen Author-Name: Yingyao Hu Author-X-Name-First: Yingyao Author-X-Name-Last: Hu Title: Identification and estimation of nonlinear models using two samples with nonclassical measurement errors Journal: Journal of Nonparametric Statistics Pages: 419-423 Issue: 4 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903556110 File-URL: http://hdl.handle.net/10.1080/10485250903556110 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:4:p:419-423 Template-Type: ReDIF-Article 1.0 Author-Name: Jafar Ahmadi Author-X-Name-First: Jafar Author-X-Name-Last: Ahmadi Author-Name: Elham Basiri Author-X-Name-First: Elham Author-X-Name-Last: Basiri Author-Name: Debasis Kundu Author-X-Name-First: Debasis Author-X-Name-Last: Kundu Title: Confidence and prediction intervals based on interpolated records Abstract: In several statistical problems, nonparametric confidence intervals for population quantiles can be constructed and their coverage probabilities can be computed exactly, but cannot in general be rendered equal to a pre-determined level. The same difficulty arises for coverage probabilities of nonparametric prediction intervals for future observations. One solution to this difficulty is to interpolate between intervals which have the closest coverage probability from above and below to the pre-determined level. In this paper, confidence intervals for population quantiles are constructed based on interpolated upper and lower records. Subsequently, prediction intervals are obtained for future upper records based on interpolated upper records. Additionally, we derive upper bounds for the coverage error of these confidence and prediction intervals. Finally, our results are applied to some real data sets. Also, a comparison via a simulation study is done with similar classical intervals obtained before. Journal: Journal of Nonparametric Statistics Pages: 1-21 Issue: 1 Volume: 29 Year: 2017 Month: 1 X-DOI: 10.1080/10485252.2016.1239826 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1239826 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:1:p:1-21 Template-Type: ReDIF-Article 1.0 Author-Name: Hammou El Barmi Author-X-Name-First: Hammou Author-X-Name-Last: El Barmi Author-Name: Ganesh Malla Author-X-Name-First: Ganesh Author-X-Name-Last: Malla Author-Name: Hari Mukerjee Author-X-Name-First: Hari Author-X-Name-Last: Mukerjee Title: Estimation of a star-shaped distribution function Abstract: A life distribution function (DF) F is said to be star-shaped if $ F(x)/x $ F(x)/x is nondecreasing on its support. This generalises the model of a convex DF, even allowing for jumps. The nonparametric maximum likelihood estimation is known to be inconsistent. We provide a uniformly strongly consistent least-squares estimator. We also derive the convergence in distribution of the estimator at a point where $ F(x)/x $ F(x)/x is increasing using the arg max theorem. Journal: Journal of Nonparametric Statistics Pages: 22-39 Issue: 1 Volume: 29 Year: 2017 Month: 1 X-DOI: 10.1080/10485252.2016.1239827 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1239827 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:1:p:22-39 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Harder Author-X-Name-First: Michael Author-X-Name-Last: Harder Author-Name: Ulrich Stadtmüller Author-X-Name-First: Ulrich Author-X-Name-Last: Stadtmüller Title: Testing exchangeability of copulas in arbitrary dimension Abstract: A test for exchangeability of copulas for arbitrary dimensions is proposed, generalising and extending a result by Genest et al. [(2012), ‘Tests of Symmetry for Bivariate Copulas’, Annals of the Institute of Statistical Mathematics, 64, 811–834]. Three test statistics together with some modifications are presented and their asymptotical behaviour is analysed. Empirical p-values are computed by using a bootstrap-procedure proposed by Rémillard and Scaillet [(2009), ‘Testing for Equality between Two Copulas’, Journal of Multivariate Analysis, 100, 377–386] and suggested by Bücher and Dette [(2010), ‘A Note on Bootstrap Approximations for the Empirical Copula Process’, Statistics & Probability Letters, 80, 1925–1932], based on a multiplier central limit theorem by van der Vaart and Wellner [(1996), Weak Convergence and Empirical Processes, Springer Series in Statistics, New York: Springer]. Finally a simulation study compares various versions of the proposed tests. Journal: Journal of Nonparametric Statistics Pages: 40-60 Issue: 1 Volume: 29 Year: 2017 Month: 1 X-DOI: 10.1080/10485252.2016.1253841 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1253841 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:1:p:40-60 Template-Type: ReDIF-Article 1.0 Author-Name: Majid Mojirsheibani Author-X-Name-First: Majid Author-X-Name-Last: Mojirsheibani Author-Name: William Pouliot Author-X-Name-First: William Author-X-Name-Last: Pouliot Title: Weighted bootstrapped kernel density estimators in two-sample problems Abstract: A weighted bootstrap method is proposed to approximate the distribution of the $ L_p $ Lp ( $ 1\leq p<\infty $ 1≤p<∞) norms of two-sample statistics involving kernel density estimators. Using an approximation theorem of Horváth, Kozkoszka and Steineback [(2000) ‘Approximations for Weighted Bootstrap Processes with an Application’, Statistics and Probability Letters, 48, 59–70], that allows one to replace the weighted bootstrap empirical process by a sequence of Gaussian processes, we establish an unconditional bootstrap central limit theorem for such statistics. The proposed method is quite straightforward to implement in practice. Furthermore, through some simulation studies, it will be shown that, depending on the weights chosen, the proposed weighted bootstrap approximation can sometimes outperform both the classical large-sample theory as well as Efron's [(1979) ‘Bootstrap Methods: Another Look at the Jackknife’, Annals of Statistics, 7, 1–26] original bootstrap algorithm. Journal: Journal of Nonparametric Statistics Pages: 61-84 Issue: 1 Volume: 29 Year: 2017 Month: 1 X-DOI: 10.1080/10485252.2016.1253842 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1253842 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:1:p:61-84 Template-Type: ReDIF-Article 1.0 Author-Name: Lydia Kara-Zaitri Author-X-Name-First: Lydia Author-X-Name-Last: Kara-Zaitri Author-Name: Ali Laksaci Author-X-Name-First: Ali Author-X-Name-Last: Laksaci Author-Name: Mustapha Rachdi Author-X-Name-First: Mustapha Author-X-Name-Last: Rachdi Author-Name: Philippe Vieu Author-X-Name-First: Philippe Author-X-Name-Last: Vieu Title: Uniform in bandwidth consistency for various kernel estimators involving functional data Abstract: The paper investigates various nonparametric models including regression, conditional distribution, conditional density and conditional hazard function, when the covariates are infinite dimensional. The main contribution is to prove uniform in bandwidth asymptotic results for kernel estimators of these functional operators. Then, the application issues, involving data-driven bandwidth selection, are discussed. Journal: Journal of Nonparametric Statistics Pages: 85-107 Issue: 1 Volume: 29 Year: 2017 Month: 1 X-DOI: 10.1080/10485252.2016.1254780 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1254780 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:1:p:85-107 Template-Type: ReDIF-Article 1.0 Author-Name: Francesco Bravo Author-X-Name-First: Francesco Author-X-Name-Last: Bravo Author-Name: Ba M. Chu Author-X-Name-First: Ba M. Author-X-Name-Last: Chu Author-Name: David T. Jacho-Chávez Author-X-Name-First: David T. Author-X-Name-Last: Jacho-Chávez Title: Semiparametric estimation of moment condition models with weakly dependent data Abstract: This paper develops the asymptotic theory for the estimation of smooth semiparametric generalized estimating equations models with weakly dependent data. The paper proposes new estimation methods based on smoothed two-step versions of the generalised method of moments and generalised empirical likelihood methods. An important aspect of the paper is that it allows the first-step estimation to have an effect on the asymptotic variances of the second-step estimators and explicitly characterises this effect for the empirically relevant case of the so-called generated regressors. The results of the paper are illustrated with a partially linear model that has not been previously considered in the literature. The proofs of the results utilise a new uniform strong law of large numbers and a new central limit theorem for U-statistics with varying kernels that are of independent interest. Journal: Journal of Nonparametric Statistics Pages: 108-136 Issue: 1 Volume: 29 Year: 2017 Month: 1 X-DOI: 10.1080/10485252.2016.1254781 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1254781 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:1:p:108-136 Template-Type: ReDIF-Article 1.0 Author-Name: Jing Sun Author-X-Name-First: Jing Author-X-Name-Last: Sun Author-Name: Yunyan Ma Author-X-Name-First: Yunyan Author-X-Name-Last: Ma Title: Empirical likelihood weighted composite quantile regression with partially missing covariates Abstract: This paper develops a novel weighted composite quantile regression (CQR) method for estimation of a linear model when some covariates are missing at random and the probability for missingness mechanism can be modelled parametrically. By incorporating the unbiased estimating equations of incomplete data into empirical likelihood (EL), we obtain the EL-based weights, and then re-adjust the inverse probability weighted CQR for estimating the vector of regression coefficients. Theoretical results show that the proposed method can achieve semiparametric efficiency if the selection probability function is correctly specified, therefore the EL weighted CQR is more efficient than the inverse probability weighted CQR. Besides, our algorithm is computationally simple and easy to implement. Simulation studies are conducted to examine the finite sample performance of the proposed procedures. Finally, we apply the new method to analyse the US news College data. Journal: Journal of Nonparametric Statistics Pages: 137-150 Issue: 1 Volume: 29 Year: 2017 Month: 1 X-DOI: 10.1080/10485252.2016.1272692 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1272692 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:1:p:137-150 Template-Type: ReDIF-Article 1.0 Author-Name: Juliane Geller Author-X-Name-First: Juliane Author-X-Name-Last: Geller Author-Name: Michael H. Neumann Author-X-Name-First: Michael H. Author-X-Name-Last: Neumann Title: Improved local polynomial estimation in time series regression Abstract: We propose a modification of local polynomial estimation which improves the efficiency of the conventional method when the observation errors are correlated. The procedure is based on a pre-transformation of the data as a generalization of the pre-whitening procedure introduced by Xiao et al. [(2003), ‘More Efficient Local Polynomial Estimation in Nonparametric Regression with Autocorrelated Errors’, Journal of the American Statistical Association, 98, 980–992]. While these authors assumed a linear process representation for the error process, we avoid any structural assumption. We further allow the regressors and the errors to be dependent. More importantly, we show that the inclusion of both leading and lagged variables in the approximation of the error terms outperforms the best approximation based on lagged variables only. Establishing its asymptotic distribution, we show that the proposed estimator is more efficient than the standard local polynomial estimator. As a by-product we prove a suitable version of a central limit theorem which allows us to improve the asymptotic normality result for local polynomial estimators by Masry and Fan [(1997), ‘Local Polynomial Estimation of Regression Functions for Mixing Processes’, Scandinavian Journal of Statistics, 24, 165–179]. A simulation study confirms the efficiency of our estimator on finite samples. An application to climate data also shows that our new method leads to an estimator with decreased variability. Journal: Journal of Nonparametric Statistics Pages: 1-27 Issue: 1 Volume: 30 Year: 2018 Month: 1 X-DOI: 10.1080/10485252.2017.1402118 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1402118 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:1:p:1-27 Template-Type: ReDIF-Article 1.0 Author-Name: Wai Leong Ng Author-X-Name-First: Wai Leong Author-X-Name-Last: Ng Author-Name: Chun Yip Yau Author-X-Name-First: Chun Yip Author-X-Name-Last: Yau Title: Test for the existence of finite moments via bootstrap Abstract: This paper develops a bootstrap hypothesis test for the existence of finite moments of a random variable, which is nonparametric and applicable to both independent and dependent data. The test is based on a property in bootstrap asymptotic theory, in which the m out of n bootstrap sample mean is asymptotically normal when the variance of the observations is finite. Consistency of the test is established. Monte Carlo simulations are conducted to illustrate the finite sample performance and compare it with alternative methods available in the literature. Applications to financial data are performed for illustration. Journal: Journal of Nonparametric Statistics Pages: 28-48 Issue: 1 Volume: 30 Year: 2018 Month: 1 X-DOI: 10.1080/10485252.2017.1402896 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1402896 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:1:p:28-48 Template-Type: ReDIF-Article 1.0 Author-Name: Salim Bouzebda Author-X-Name-First: Salim Author-X-Name-Last: Bouzebda Author-Name: Chrysanthi Papamichail Author-X-Name-First: Chrysanthi Author-X-Name-Last: Papamichail Author-Name: Nikolaos Limnios Author-X-Name-First: Nikolaos Author-X-Name-Last: Limnios Title: On a multidimensional general bootstrap for empirical estimator of continuous-time semi-Markov kernels with applications Abstract: The present paper introduces a general notion and presents results of bootstrapped empirical estimators of the semi-Markov kernels and of the conditional transition distributions for semi-Markov processes with countable state space, constructed by exchangeably weighting the sample. Our proposal provides a unification of bootstrap methods in the semi-Markov setting including, in particular, Efron's bootstrap. Asymptotic properties of these generalised bootstrapped empirical distributions are obtained, under mild conditions by a martingale approach. We also obtain some new results on the weak convergence of the empirical semi-Markov processes. We apply these general results in several statistical problems such as the construction of confidence bands and the goodness-of-fit tests where the limiting distributions are derived under the null hypothesis. Finally, we introduce the quantile estimators and their bootstrapped versions in the semi-Markov framework and we establish their limiting laws by using the functional delta methods. Our theoretical results and numerical examples by simulations demonstrate the merits of the proposed techniques. Journal: Journal of Nonparametric Statistics Pages: 49-86 Issue: 1 Volume: 30 Year: 2018 Month: 1 X-DOI: 10.1080/10485252.2017.1404059 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1404059 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:1:p:49-86 Template-Type: ReDIF-Article 1.0 Author-Name: Anna E. Dudek Author-X-Name-First: Anna E. Author-X-Name-Last: Dudek Title: Block bootstrap for periodic characteristics of periodically correlated time series Abstract: This research is dedicated to the study of periodic characteristics of periodically correlated time series such as seasonal means, seasonal variances and autocovariance functions. Two bootstrap methods are used: the extension of the usual Moving Block Bootstrap (EMBB) and the Generalised Seasonal Block Bootstrap (GSBB). The first approach is proposed, because the usual Moving Block Bootstrap does not preserve the periodic structure contained in the data and cannot be applied for the considered problems. For the aforementioned periodic characteristics the bootstrap estimators are introduced and consistency of the EMBB in all cases is obtained. Moreover, the GSBB consistency results for seasonal variances and autocovariance function are presented. Additionally, the bootstrap consistency of both considered techniques for smooth functions of the parameters of interest is obtained. Finally, the simultaneous bootstrap confidence intervals are constructed. A simulation study to compare their actual coverage probabilities is provided. A real data example is presented. Journal: Journal of Nonparametric Statistics Pages: 87-124 Issue: 1 Volume: 30 Year: 2018 Month: 1 X-DOI: 10.1080/10485252.2017.1404060 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1404060 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:1:p:87-124 Template-Type: ReDIF-Article 1.0 Author-Name: Tao Huang Author-X-Name-First: Tao Author-X-Name-Last: Huang Author-Name: Jialiang Li Author-X-Name-First: Jialiang Author-X-Name-Last: Li Title: Semiparametric model average prediction in panel data analysis Abstract: Forecasting in economic data analysis is dominated by linear prediction methods where the predicted values are calculated from a fitted linear regression model. With multiple predictor variables, multivariate nonparametric models were proposed in the literature. However, empirical studies indicate the prediction performance of multi-dimensional nonparametric models may be unsatisfactory. We propose a new semiparametric model average prediction (SMAP) approach to analyse panel data and investigate its prediction performance with numerical examples. Estimation of individual covariate effect only requires univariate smoothing and thus may be more stable than previous multivariate smoothing approaches. The estimation of optimal weight parameters incorporates the longitudinal correlation and the asymptotic properties of the estimated results are carefully studied in this paper. Journal: Journal of Nonparametric Statistics Pages: 125-144 Issue: 1 Volume: 30 Year: 2018 Month: 1 X-DOI: 10.1080/10485252.2017.1404061 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1404061 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:1:p:125-144 Template-Type: ReDIF-Article 1.0 Author-Name: Xu-Guo Ye Author-X-Name-First: Xu-Guo Author-X-Name-Last: Ye Author-Name: Jin-Guan Lin Author-X-Name-First: Jin-Guan Author-X-Name-Last: Lin Author-Name: Yan-Yong Zhao Author-X-Name-First: Yan-Yong Author-X-Name-Last: Zhao Title: A two-step estimation of diffusion processes using noisy observations Abstract: This paper considers the estimation of unknown drift and diffusion functions of a one-dimensional diffusion process $ X_{t} $ Xt when the observation $ Y_{t} $ Yt is a discrete sampling of $ X_{t} $ Xt with an additive noise, at times $ i\delta $ iδ, $ i=1, \ldots, N $ i=1,…,N. In order to reduce the noise effect, a two-step estimation method is proposed based on the joint use of the pre-averaging technique and kernel smoothing. Under some suitable conditions, the proposed estimators are consistent and asymptotically normal. A simulation study and a real data application are given to evaluate the finite sample performance of the proposed method in comparison with alternative methods. Journal: Journal of Nonparametric Statistics Pages: 145-181 Issue: 1 Volume: 30 Year: 2018 Month: 1 X-DOI: 10.1080/10485252.2017.1404062 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1404062 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:1:p:145-181 Template-Type: ReDIF-Article 1.0 Author-Name: Guoxin Qiu Author-X-Name-First: Guoxin Author-X-Name-Last: Qiu Author-Name: Kai Jia Author-X-Name-First: Kai Author-X-Name-Last: Jia Title: Extropy estimators with applications in testing uniformity Abstract: Two estimators for estimating the extropy of an absolutely continuous random variable with known support were introduced by using spacing. It is shown that the proposed estimators are consistent and their mean square errors are shift invariant. Their behaviours were also studied by means of real data and Monte Carlo simulation. The winner estimator of extropy in the Monte Carlo experiment was used to develop goodness-of-fit test for standard uniform distribution. It is shown that the extropy-based test that we proposed performs well by comparing its powers with that of other tests for uniformity. Journal: Journal of Nonparametric Statistics Pages: 182-196 Issue: 1 Volume: 30 Year: 2018 Month: 1 X-DOI: 10.1080/10485252.2017.1404063 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1404063 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:1:p:182-196 Template-Type: ReDIF-Article 1.0 Author-Name: Yoonsuh Jung Author-X-Name-First: Yoonsuh Author-X-Name-Last: Jung Title: Multiple predicting K-fold cross-validation for model selection Abstract: K-fold cross-validation (CV) is widely adopted as a model selection criterion. In K-fold CV, $ (K-1) $ (K−1) folds are used for model construction and the hold-out fold is allocated to model validation. This implies model construction is more emphasised than the model validation procedure. However, some studies have revealed that more emphasis on the validation procedure may result in improved model selection. Specifically, leave-m-out CV with n samples may achieve variable-selection consistency when m/n approaches to 1. In this study, a new CV method is proposed within the framework of K-fold CV. The proposed method uses $ (K-1) $ (K−1) folds of the data for model validation, while the other fold is for model construction. This provides $ (K-1) $ (K−1) predicted values for each observation. These values are averaged to produce a final predicted value. Then, the model selection based on the averaged predicted values can reduce variation in the assessment due to the averaging. The variable-selection consistency of the suggested method is established. Its advantage over K-fold CV with finite samples are examined under linear, non-linear, and high-dimensional models. Journal: Journal of Nonparametric Statistics Pages: 197-215 Issue: 1 Volume: 30 Year: 2018 Month: 1 X-DOI: 10.1080/10485252.2017.1404598 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1404598 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:1:p:197-215 Template-Type: ReDIF-Article 1.0 Author-Name: Tianlei Chen Author-X-Name-First: Tianlei Author-X-Name-Last: Chen Author-Name: Pang Du Author-X-Name-First: Pang Author-X-Name-Last: Du Title: Mixture cure rate models with accelerated failures and nonparametric form of covariate effects Abstract: Two-component mixture cure rate model is popular in cure rate data analysis with the proportional hazards and accelerated failure time (AFT) models being the major competitors for modelling the latency component. [Wang, L., Du, P., and Liang, H. (2012), ‘Two-Component Mixture Cure Rate Model with Spline Estimated Nonparametric Components’, Biometrics, 68, 726–735] first proposed a nonparametric mixture cure rate model where the latency component assumes proportional hazards with nonparametric covariate effects in the relative risk. Here we consider a mixture cure rate model where the latency component assumes AFTs with nonparametric covariate effects in the acceleration factor. Besides the more direct physical interpretation than the proportional hazards, our model has an additional scalar parameter which adds more complication to the computational algorithm as well as the asymptotic theory. We develop a penalised EM algorithm for estimation together with confidence intervals derived from the Louis formula. Asymptotic convergence rates of the parameter estimates are established. Simulations and the application to a melanoma study shows the advantages of our new method. Journal: Journal of Nonparametric Statistics Pages: 216-237 Issue: 1 Volume: 30 Year: 2018 Month: 1 X-DOI: 10.1080/10485252.2017.1404599 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1404599 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:1:p:216-237 Template-Type: ReDIF-Article 1.0 Author-Name: Madison Giacofci Author-X-Name-First: Madison Author-X-Name-Last: Giacofci Author-Name: Sophie Lambert-Lacroix Author-X-Name-First: Sophie Author-X-Name-Last: Lambert-Lacroix Author-Name: Franck Picard Author-X-Name-First: Franck Author-X-Name-Last: Picard Title: Minimax wavelet estimation for multisample heteroscedastic nonparametric regression Abstract: The problem of estimating the baseline signal from multisample noisy curves is investigated. We consider the functional mixed-effects model, and we suppose that the functional fixed effect belongs to the Besov class. This framework allows us to model curves that can exhibit strong irregularities, such as peaks or jumps for instance. The lower bound for the $ L_2 $ L2 minimax risk is provided, as well as the upper bound of the minimax rate, that is derived by constructing a wavelet estimator for the functional fixed effect. Our work constitutes the first theoretical functional results in multisample nonparametric regression. Our approach is illustrated on realistic simulated datasets as well as on experimental data. Journal: Journal of Nonparametric Statistics Pages: 238-261 Issue: 1 Volume: 30 Year: 2018 Month: 1 X-DOI: 10.1080/10485252.2017.1406091 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1406091 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:1:p:238-261 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Corrigendum Journal: Journal of Nonparametric Statistics Pages: x-x Issue: 1 Volume: 30 Year: 2018 Month: 1 X-DOI: 10.1080/10485252.2017.1414013 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1414013 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:30:y:2018:i:1:p:x-x Template-Type: ReDIF-Article 1.0 Author-Name: Marie Hušková Author-X-Name-First: Marie Author-X-Name-Last: Hušková Author-Name: Simos Meintanis Author-X-Name-First: Simos Author-X-Name-Last: Meintanis Title: Tests for the multivariate -sample problem based on the empirical characteristic function Abstract: Tests for the multivariate k-sample problem are considered. The tests are based on the weighted L2 distance between empirical characteristic functions, and afford an interesting interpretation in terms of a corresponding test statistic based on the L2 distance of pairs of non-parametric density estimators. Depending on the choice of weighting, a corresponding Dirac-type weight function reduces the test to a normalised version of the L2 distance between the sample means of the k populations. Theoretical and computational issues are considered, while the finite-sample implementation based on the permutation distribution of the test statistic shows that the new test performs well in comparison with alternative procedures of the change-point type. Journal: Journal of Nonparametric Statistics Pages: 263-277 Issue: 3 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250801948294 File-URL: http://hdl.handle.net/10.1080/10485250801948294 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:3:p:263-277 Template-Type: ReDIF-Article 1.0 Author-Name: P.L. Davies Author-X-Name-First: P.L. Author-X-Name-Last: Davies Author-Name: M. Meise Author-X-Name-First: M. Author-X-Name-Last: Meise Title: Approximating data with weighted smoothing splines Abstract: Given a data set (ti, yi), i=1, ˙s, n with ti∈[0, 1] non-parametric regression is concerned with the problem of specifying a suitable function fn:[0, 1]→ℝ such that the data can be reasonably approximated by the points (ti, fn(ti)), i=1, ˙s, n. If a data set exhibits large variations in local behaviour, for example large peaks as in spectroscopy data, then the method must be able to adapt to the local changes in smoothness. Whilst many methods are able to accomplish this, they are less successful at adapting derivatives. In this paper we showed how the goal of local adaptivity of the function and its first and second derivatives can be attained in a simple manner using weighted smoothing splines. A residual-based concept of approximation is used which forces local adaptivity of the regression function together with a global regularization which makes the function as smooth as possible subject to the approximation constraints. Journal: Journal of Nonparametric Statistics Pages: 207-228 Issue: 3 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250801948625 File-URL: http://hdl.handle.net/10.1080/10485250801948625 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:3:p:207-228 Template-Type: ReDIF-Article 1.0 Author-Name: Jiezhun Gu Author-X-Name-First: Jiezhun Author-X-Name-Last: Gu Author-Name: Subhashis Ghosal Author-X-Name-First: Subhashis Author-X-Name-Last: Ghosal Title: Strong approximations for resample quantile processes and application to ROC methodology Abstract: The receiver operating characteristic (ROC) curve is defined as true positive rate versus false positive rate obtained by varying a decision threshold criterion. It has been widely used in medical sciences for its ability to measure the accuracy of diagnostic or prognostic tests. Mathematically speaking, ROC curve is the composition of survival function of one population with the quantile function of another population. In this paper, we study strong approximation for the quantile processes of the Bayesian bootstrap (BB) resampling distributions, and use this result to study strong approximations for the BB version of the ROC process in terms of two independent Kiefer processes. The results imply asymptotically accurate coverage probabilities for the confidence bands for the ROC curve and confidence intervals for the area under the curve functional of the ROC constructed using the BB method. Similar results follow for the bootstrap resampling distribution. Journal: Journal of Nonparametric Statistics Pages: 229-240 Issue: 3 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250801954128 File-URL: http://hdl.handle.net/10.1080/10485250801954128 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:3:p:229-240 Template-Type: ReDIF-Article 1.0 Author-Name: Abbas Alhakim Author-X-Name-First: Abbas Author-X-Name-Last: Alhakim Author-Name: William Hooper Author-X-Name-First: William Author-X-Name-Last: Hooper Title: A non-parametric test for several independent samples Abstract: We introduce a large sample non-parametric test for the hypothesis of equal distributions of three or more independent samples. The test can be considered as a generalisation of the two sample run tests of Wald and Wolfowitz in that it sorts the data and replaces the values with the ‘label’ of the sample from which they come, thus transforming the problem to a question about the randomness of the resulting pooled sample. The test statistic and its asymptotic null distribution are derived using the central limit theorem of finite Markov chains. Simulation results and comparisons with the standard k-sample Kruskal–Wallis and Kolmogorov–Smirnov tests are given. One particular strength of the test is that it is capable of distinguishing between different distributions having the same mean in a few cases when the Kruskal–Wallis test is completely paralysed. Journal: Journal of Nonparametric Statistics Pages: 253-261 Issue: 3 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250801976741 File-URL: http://hdl.handle.net/10.1080/10485250801976741 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:3:p:253-261 Template-Type: ReDIF-Article 1.0 Author-Name: Brent Johnson Author-X-Name-First: Brent Author-X-Name-Last: Johnson Author-Name: Limin Peng Author-X-Name-First: Limin Author-X-Name-Last: Peng Title: Rank-based variable selection Abstract: This note considers variable selection in the robust linear model via R-estimates. The proposed rank-based approach is a generalisation of the penalised least-squares estimators where we replace the least-squares loss function with Jaeckel's (1972) dispersion function. Our rank-based method is robust to outliers in the errors and has roots in traditional non-parametric statistics for simple location-shift problems. We establish the theoretical properties of our estimators which ensure desirable asymptotic behaviour of setting coefficient estimates to zero for unimportant variables and consistently estimating coefficients for important variables. Numerical studies indicate that the rank-based methods perform well for both light- and heavy-tailed error distributions. Journal: Journal of Nonparametric Statistics Pages: 241-252 Issue: 3 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250801998950 File-URL: http://hdl.handle.net/10.1080/10485250801998950 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:3:p:241-252 Template-Type: ReDIF-Article 1.0 Author-Name: Winfried Stute Author-X-Name-First: Winfried Author-X-Name-Last: Stute Title: Almost sure representations of weighted -statistics with applications Abstract: Let X1, …, Xn be a sample of i.i.d. random variables on the real line. In this paper, we introduce and study weighted U-statistics of the type Sn=(n(n−1))−1 ∑i¬=j J(i/n+1, j/n+1) h(Xi:n, Xj:n), where J and h are given bivariate functions and X1:n≤···≤Xn:n are the pertaining order statistics of the sample. Under weak integrability conditions on Jh, we derive an almost sure representation of Sn in terms of a U-statistic and a remainder which is roughly of the order n−1. Specification of J and h yields representations for L-statistics and various robust measures of spread. The method also applies in a two-sample as well as in a censored data situation. Journal: Journal of Nonparametric Statistics Pages: 191-205 Issue: 3 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250801999438 File-URL: http://hdl.handle.net/10.1080/10485250801999438 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:3:p:191-205 Template-Type: ReDIF-Article 1.0 Author-Name: Somnath Datta Author-X-Name-First: Somnath Author-X-Name-Last: Datta Author-Name: Jaakko Nevalainen Author-X-Name-First: Jaakko Author-X-Name-Last: Nevalainen Author-Name: Hannu Oja Author-X-Name-First: Hannu Author-X-Name-Last: Oja Title: A general class of signed-rank tests for clustered data when the cluster size is potentially informative Abstract: Rank-based tests are alternatives to likelihood-based tests popularised by their relative robustness and underlying elegant mathematical theory. There has been a surge in research activities in this area in recent years since a number of researchers are working to develop and extend rank-based procedures to clustered-dependent data which include situations with known correlation structures (e.g. as in mixed effects models) as well as more general form of dependence. The purpose of this paper is to test the symmetry of a marginal distribution under clustered data. However, unlike most other papers in the area, we consider the possibility that the cluster size is a random variable whose distribution is dependent on the distribution of the variable of interest within a cluster. This situation typically arises when the clusters are defined in a natural way (e.g. not controlled by the experimenter or statistician) and in which the size of the cluster may carry information about the distribution of data values within a cluster. Under the scenario of an informative cluster size, attempts to use some form of variance-adjusted sign or signed-rank tests would fail since they would not maintain the correct size under the distribution of marginal symmetry. To overcome this difficulty, Datta and Satten [2008, ‘A Signed-Rank Test for Clustered Data’, Biometrics, 64, 501–507] proposed a Wilcoxon-type signed-rank test based on the principle of within-cluster resampling. In this paper, we study this problem in more generality by introducing a class of valid tests employing a general score function. Asymptotic null distribution of these tests is obtained. A simulation study shows that a more general choice of the score function can sometimes result in greater power than the Datta and Satten test; furthermore, this development offers the user a wider choice. We illustrate our tests using a real data example on spinal cord injury (SCI) patients. Journal: Journal of Nonparametric Statistics Pages: 797-808 Issue: 3 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.672647 File-URL: http://hdl.handle.net/10.1080/10485252.2012.672647 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:797-808 Template-Type: ReDIF-Article 1.0 Author-Name: Arnab Maity Author-X-Name-First: Arnab Author-X-Name-Last: Maity Title: A powerful test for comparing multiple regression functions Abstract: In this article, we address the important problem of comparison of two or more population regression functions. Recently, Pardo-Fernández, Van Keilegom and González-Manteiga [2007, ‘Testing for Equality of k Regression Curves’, Statistica Sinica, 17, 1115–1137] developed test statistics for simple nonparametric regression models: Yij=θj(Zij)+σj(Zij)εij, based on empirical distributions of the errors in each population j=1, …, J. In this article, we propose a test for equality of the θj(·) based on the concept of generalised likelihood ratio type statistics. We also generalise our test for other nonparametric regression set-ups, for example, nonparametric logistic regression, where the log-likelihood for population j is any general smooth function ℒ{Yj, θj(Zj)}. We describe a resampling procedure to obtain the critical values of the test. In addition, we present a simulation study to evaluate the performance of the proposed test and compare our results to those in Pardo-Fernández et al. [2007, ‘Testing for Equality of k Regression Curves’, Statistica Sinica, 17, 1115–1137]. Journal: Journal of Nonparametric Statistics Pages: 563-576 Issue: 3 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.677842 File-URL: http://hdl.handle.net/10.1080/10485252.2012.677842 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:563-576 Template-Type: ReDIF-Article 1.0 Author-Name: Robin Genuer Author-X-Name-First: Robin Author-X-Name-Last: Genuer Title: Variance reduction in purely random forests Abstract: Random forests (RFs), introduced by Leo Breiman in 2001, are a very effective statistical method. The complex mechanism of the method makes theoretical analysis difficult. Therefore, simplified versions of RF, called purely RFs (PRF), which can be theoretically handled more easily, have been considered. In this paper, we study the variance of such forests. First, we show a general upper bound which emphasises the fact that a forest reduces the variance. We then introduce a simple variant of PRFs, that we call purely uniformly RFs. For this variant and in the context of regression problems with a one-dimensional predictor space, we show that both random trees and RFs reach minimax rate of convergence. In addition, we prove that compared with random trees, RFs improve accuracy by reducing the estimator variance by a factor of three-fourths. Journal: Journal of Nonparametric Statistics Pages: 543-562 Issue: 3 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.677843 File-URL: http://hdl.handle.net/10.1080/10485252.2012.677843 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:543-562 Template-Type: ReDIF-Article 1.0 Author-Name: N. Zougab Author-X-Name-First: N. Author-X-Name-Last: Zougab Author-Name: S. Adjabi Author-X-Name-First: S. Author-X-Name-Last: Adjabi Author-Name: C. Kokonendji Author-X-Name-First: C. Author-X-Name-Last: Kokonendji Title: Binomial kernel and Bayes local bandwidth in discrete function estimation Abstract: The Bayesian approach to bandwidth selection in discrete associated kernel estimation of probability mass function is a very good alternative to the classical popular methods such as the methods which adopt the asymptotic mean integrated squared error as a criterion and the cross-validation technique. In this paper, we propose a Bayesian local approach to bandwidth selection considering the binomial kernel estimator and locally treating the bandwidth h as a random quantity with a prior distribution. The local bandwidth is estimated by the posterior mean of h. The performance of this proposed approach and that of the classical methods are compared using simulations of data generated from known discrete functions. The new method is then applied to a real count data set. The smoothing quality of the Bayes estimator is very satisfactory. Journal: Journal of Nonparametric Statistics Pages: 783-795 Issue: 3 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.678847 File-URL: http://hdl.handle.net/10.1080/10485252.2012.678847 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:783-795 Template-Type: ReDIF-Article 1.0 Author-Name: Weixin Yao Author-X-Name-First: Weixin Author-X-Name-Last: Yao Author-Name: Bruce Lindsay Author-X-Name-First: Bruce Author-X-Name-Last: Lindsay Author-Name: Runze Li Author-X-Name-First: Runze Author-X-Name-Last: Li Title: Local modal regression Abstract: A local modal estimation procedure is proposed for the regression function in a nonparametric regression model. A distinguishing characteristic of the proposed procedure is that it introduces an additional tuning parameter that is automatically selected using the observed data in order to achieve both robustness and efficiency of the resulting estimate. We demonstrate both theoretically and empirically that the resulting estimator is more efficient than the ordinary local polynomial regression (LPR) estimator in the presence of outliers or heavy-tail error distribution (such as t-distribution). Furthermore, we show that the proposed procedure is as asymptotically efficient as the LPR estimator when there are no outliers and the error distribution is a Gaussian distribution. We propose an expectation–maximisation-type algorithm for the proposed estimation procedure. A Monte Carlo simulation study is conducted to examine the finite sample performance of the proposed method. The simulation results confirm the theoretical findings. The proposed methodology is further illustrated via an analysis of a real data example. Journal: Journal of Nonparametric Statistics Pages: 647-663 Issue: 3 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.678848 File-URL: http://hdl.handle.net/10.1080/10485252.2012.678848 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:647-663 Template-Type: ReDIF-Article 1.0 Author-Name: Samiran Sinha Author-X-Name-First: Samiran Author-X-Name-Last: Sinha Title: A functional method for the conditional logistic regression with errors-in-covariates Abstract: In this article, we develop a functional approach for handling errors-in-covariates in matched case–control studies which are commonly analysed through the conditional logistic regression. We propose to estimate the parameters from a set of unbiased estimating equations. We require that the moment-generating function of the measurement errors exists. We investigate the asymptotic properties of the estimators. The finite sample performance of the method is judged via simulation studies. The proposed methodology is illustrated by analysing the data from the NIH-AARP Diet and Health study. Journal: Journal of Nonparametric Statistics Pages: 577-595 Issue: 3 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.687735 File-URL: http://hdl.handle.net/10.1080/10485252.2012.687735 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:577-595 Template-Type: ReDIF-Article 1.0 Author-Name: S. Goh Author-X-Name-First: S. Author-X-Name-Last: Goh Title: Design-adaptive nonparametric estimation of conditional quantile derivatives Abstract: This paper proposes a new approach to constructing nonparametric estimators of conditional quantile functions and their derivatives with respect to conditioning variables. The new approach is intended specifically to produce estimators with biases that do not depend on the design density. This is in marked contrast to more conventional nonparametric estimators based on locally polynomial quantile regressions, the biases of which are characterised by asymptotic expansions in which the design density appears, at least at some order of approximation. The specific approach taken in this paper involves the kernel smoothing of the ratio of a preliminary nonparametric estimate of the conditional quantile function to another preliminary nonparametric estimate of the design density. Monte Carlo evidence indicates that the proposed estimators compare favourably to nonparametric estimators based on local polynomials. An empirical example exploring the relationship between individual earnings and age is also included. Additional technical details are contained in supplementary material available online. Journal: Journal of Nonparametric Statistics Pages: 597-612 Issue: 3 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.688826 File-URL: http://hdl.handle.net/10.1080/10485252.2012.688826 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:597-612 Template-Type: ReDIF-Article 1.0 Author-Name: Nikolai Ushakov Author-X-Name-First: Nikolai Author-X-Name-Last: Ushakov Author-Name: Anastasia Ushakova Author-X-Name-First: Anastasia Author-X-Name-Last: Ushakova Title: On density estimation with superkernels Abstract: In this article, we consider the problem of nonparametric density estimation in the case, when the original sample has a large size, but the data are given in a binned form, i.e. in the form of a histogram. Such situations are typical for many physical problems, in particular, in scanning electron microscopy and electron beam lithography. We study how superkernels can be used in such situations. It is shown that superkernels can be essentially superior over conventional kernels not only for very smooth densities. The problem of bandwidth and bin width selection is also considered. Journal: Journal of Nonparametric Statistics Pages: 613-627 Issue: 3 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.688969 File-URL: http://hdl.handle.net/10.1080/10485252.2012.688969 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:613-627 Template-Type: ReDIF-Article 1.0 Author-Name: Yijie Xue Author-X-Name-First: Yijie Author-X-Name-Last: Xue Author-Name: Nicole Lazar Author-X-Name-First: Nicole Author-X-Name-Last: Lazar Title: Empirical likelihood-based hot deck imputation methods Abstract: The non-response problem commonly exists in survey data and has been investigated by various methods. We propose an empirical likelihood-based hot deck imputation method, which resamples the observed data by using the weights from the empirical likelihood ratio for missing values. We demonstrate that the estimator of the mean is unbiased and the corresponding variance estimator of the mean is asymptotically unbiased under mild conditions. Next, we extend our method for U-statistic estimators and show that the estimator converges to the real U-statistic in probability. The proposed method can also incorporate multiple imputations and/or regression imputations easily. Simulations and a real example illustrate that our method outperforms some of the existing approaches, such as simple hot deck imputation and fractional hot deck imputation. We conclude with a discussion of the advantages of the empirical likelihood-based hot deck imputation method. Journal: Journal of Nonparametric Statistics Pages: 629-646 Issue: 3 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.690879 File-URL: http://hdl.handle.net/10.1080/10485252.2012.690879 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:629-646 Template-Type: ReDIF-Article 1.0 Author-Name: Heeyoung Kim Author-X-Name-First: Heeyoung Author-X-Name-Last: Kim Author-Name: Xiaoming Huo Author-X-Name-First: Xiaoming Author-X-Name-Last: Huo Title: Locally optimal adaptive smoothing splines Abstract: Smoothing splines are widely used for estimating an unknown function in the nonparametric regression. If data have large spatial variations, however, the standard smoothing splines (which adopt a global smoothing parameter λ) perform poorly. Adaptive smoothing splines adopt a variable smoothing parameter λ(x) (i.e. the smoothing parameter is a function of the design variable x) to adapt to varying roughness. In this paper, we derive an asymptotically optimal local penalty function for λ(x)∈C3 under suitable conditions. The derived locally optimal penalty function in turn is used for the development of a locally optimal adaptive smoothing spline estimator. In the numerical study, we show that our estimator performs very well using several simulated and real data sets. Journal: Journal of Nonparametric Statistics Pages: 665-680 Issue: 3 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.693610 File-URL: http://hdl.handle.net/10.1080/10485252.2012.693610 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:665-680 Template-Type: ReDIF-Article 1.0 Author-Name: Yujiao Yang Author-X-Name-First: Yujiao Author-X-Name-Last: Yang Author-Name: Yuhang Xu Author-X-Name-First: Yuhang Author-X-Name-Last: Xu Author-Name: Qiongxia Song Author-X-Name-First: Qiongxia Author-X-Name-Last: Song Title: Spline confidence bands for variance functions in nonparametric time series regressive models Abstract: For nonparametric time series regression, we propose to apply polynomial splines to squared residuals to develop the variance function estimation. Furthermore, we obtain and use simultaneous confidence bands to detect certain parametric forms for entire variance curves. The proposed method is extremely fast. Asymptotic results are established under the assumption that observations are from a strictly stationary $\alpha$-mixing process. Simulations and a financial data set application are provided to illustrate the performance of the proposed method numerically. Journal: Journal of Nonparametric Statistics Pages: 699-714 Issue: 3 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.693925 File-URL: http://hdl.handle.net/10.1080/10485252.2012.693925 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:699-714 Template-Type: ReDIF-Article 1.0 Author-Name: Qiqing Yu Author-X-Name-First: Qiqing Author-X-Name-Last: Yu Author-Name: Jiahui Li Author-X-Name-First: Jiahui Author-X-Name-Last: Li Title: THE NPMLE of the joint distribution function with right-censored and masked competing risks data Abstract: Even though the right-censored competing risks data with masked failure cause have been studied for 30 years, the asymptotic properties of the nonparametric maximum-likelihood estimator (NPMLE) of the joint distribution function with such data have never been studied. We show that the solution to the NPMLE is not unique, and the NPMLE proposed in the current literature is inconsistent. Moreover, we construct a consistent NPMLE and establish its asymptotic normality. It is a non-trivial example in the survival analysis context that there exist an inconsistent NPMLE as well as another consistent NPMLE with the same data and under the same model. Our proofs do not need the symmetry assumption made by almost all researchers on such data. We present simulation results on the consistent NPMLE and apply the NPMLE to a data set in medical research. Journal: Journal of Nonparametric Statistics Pages: 753-764 Issue: 3 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.695782 File-URL: http://hdl.handle.net/10.1080/10485252.2012.695782 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:753-764 Template-Type: ReDIF-Article 1.0 Author-Name: Zhao Chen Author-X-Name-First: Zhao Author-X-Name-Last: Chen Author-Name: Runze Li Author-X-Name-First: Runze Author-X-Name-Last: Li Author-Name: Yaohua Wu Author-X-Name-First: Yaohua Author-X-Name-Last: Wu Title: Weighted quantile regression for AR model with infinite variance errors Abstract: Autoregressive (AR) models with finite variance errors have been well studied. This paper is concerned with AR models with heavy-tailed errors, which is useful in various scientific research areas. Statistical estimation for AR models with infinite variance errors is very different from those for AR models with finite variance errors. In this paper, we consider a weighted quantile regression for AR models to deal with infinite variance errors. We further propose an induced smoothing method to deal with computational challenges in weighted quantile regression. We show that the difference between weighted quantile regression estimate and its smoothed version is negligible. We further propose a test for linear hypothesis on the regression coefficients. We conduct Monte Carlo simulation study to assess the finite sample performance of the proposed procedures. We illustrate the proposed methodology by an empirical analysis of a real-life data set. Journal: Journal of Nonparametric Statistics Pages: 715-731 Issue: 3 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.698280 File-URL: http://hdl.handle.net/10.1080/10485252.2012.698280 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:715-731 Template-Type: ReDIF-Article 1.0 Author-Name: Akim Adekpedjou Author-X-Name-First: Akim Author-X-Name-Last: Adekpedjou Author-Name: Edsel Peña Author-X-Name-First: Edsel Author-X-Name-Last: Peña Title: Semiparametric estimation with recurrent event data under informative monitoring Abstract: Consider a study where the times of occurrences of a recurrent event for n units are monitored. For the ith unit, Ti1, Ti2, …, denote the successive event inter-occurrence times and this unit is monitored over a random period [0, τi] with τi independent of the Tijs. Over this monitoring period, is the random number of event occurrences. The Tijs are independent and identically distributed (IID) from an unknown continuous distribution function F and the τis are IID from a distribution function G. A generalised Koziol–Green (GKG) structure wherein 1−G=(1−F)β for some β>0 is assumed. Under this model, Nelson–Aalen and product-limit type estimators of Λ=−log(1−F) and F are obtained, as well as an estimator of β. Asymptotic and small-sample properties of these estimators are obtained and the estimator of F is compared to the fully nonparametric estimator in Peña et al. [(2001), ‘Nonparametric Estimation with Recurrent Event Data’, Journal of the American Statistical Association, 96, 1299–1315] in terms of their finite-sample and asymptotic efficiency. The performance of the estimators of F are also examined when the GKG structure does not hold through a simulation study. Journal: Journal of Nonparametric Statistics Pages: 733-752 Issue: 3 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.698281 File-URL: http://hdl.handle.net/10.1080/10485252.2012.698281 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:733-752 Template-Type: ReDIF-Article 1.0 Author-Name: Gaorong Li Author-X-Name-First: Gaorong Author-X-Name-Last: Li Author-Name: Liugen Xue Author-X-Name-First: Liugen Author-X-Name-Last: Xue Author-Name: Heng Lian Author-X-Name-First: Heng Author-X-Name-Last: Lian Title: SCAD-penalised generalised additive models with non-polynomial dimensionality Abstract: In this article, we study the (group) smoothly clipped absolute deviation (SCAD) estimator in the estimation of generalised additive models. The SCAD penalty, proposed by Fan and Li [(2001) ‘Variable Selection via Nonconcave Penalised Likelihood and Its Oracle Properties’, Journal of the American Statistical Association 96(456), 1348–1360], has many desirable properties including continuity, sparsity and unbiasedness. For high-dimensional parametric models, it has only recently been shown that the SCAD estimator can deal with problems with dimensions much larger than the sample size. Here, we show that the SCAD estimator can be successfully applied to generalised additive models with non-polynomial dimensionality and our study represents the first such result for the SCAD estimator in nonparametric problems, as far as we know. In particular, under suitable assumptions, we theoretically show that the dimension of the problem can be close to exp<texlscub>nd/(2d+1)</texlscub>, where n is the sample size and d is the smoothness parameter of the component functions. Some Monte Carlo studies and a real data application are also presented. Journal: Journal of Nonparametric Statistics Pages: 681-697 Issue: 3 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.698740 File-URL: http://hdl.handle.net/10.1080/10485252.2012.698740 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:681-697 Template-Type: ReDIF-Article 1.0 Author-Name: Jingle Wang Author-X-Name-First: Jingle Author-X-Name-Last: Wang Author-Name: Ming Zheng Author-X-Name-First: Ming Author-X-Name-Last: Zheng Title: Wavelet detection of change points in hazard rate models with censored dependent data Abstract: The detection of change points in hazard rate has been studied a lot for independently and identically distributed survival data. However, in some domains, the survival times may be dependent. This paper considers the detection and estimation of change points in hazard rate for censored dependent data. We construct a nonparametric test statistic based on the wavelet method for change point detection. We also utilise the test statistic to design estimators for the number, the locations, and the jump sizes of the change points in hazard rate. The corresponding asymptotic properties are derived. Some simulation studies are conducted to assess the finite sample performances of the proposed method. Journal: Journal of Nonparametric Statistics Pages: 765-781 Issue: 3 Volume: 24 Year: 2012 X-DOI: 10.1080/10485252.2012.700055 File-URL: http://hdl.handle.net/10.1080/10485252.2012.700055 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:765-781 Template-Type: ReDIF-Article 1.0 Author-Name: Fortunato Pesarin Author-X-Name-First: Fortunato Author-X-Name-Last: Pesarin Author-Name: Luigi Salmaso Author-X-Name-First: Luigi Author-X-Name-Last: Salmaso Title: Finite-sample consistency of combination-based permutation tests with application to repeated measures designs Abstract: In several application fields, e.g. genetics, image and functional analysis, several biomedical and social experimental and observational studies, etc. it may happen that the number of observed variables is much larger than that of subjects. It can be proved that, for a given and fixed number of subjects, when the number of variables increases and the noncentrality parameter of the underlying population distribution increases with respect to each added variable, then power of multivariate permutation tests based on Pesarin's combining functions [Pesarin, F. (2001), Multivariate Permutation Tests with Applications in Biostatistics, New York: Wiley, Chichester] is monotonically increasing. These results confirm and extend those presented by [Blair, Higgins, Karniski and Kromrey (1994), ‘A Study of Multivariate Permutation Tests which May Replace Hotelling's T2 Test in Prescribed Circumstances’, Multivariate Behavioral Research 29, 141–163]. Moreover, they allow us to introduce the property of finite-sample consistency for those kinds of combination-based permutation tests. Sufficient conditions are given in order that the rejection rate converges to one, for fixed sample sizes at any attainable α -values, when the number of variables diverges. A simulation study and a real case study are presented. Journal: Journal of Nonparametric Statistics Pages: 669-684 Issue: 5 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250902807407 File-URL: http://hdl.handle.net/10.1080/10485250902807407 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:5:p:669-684 Template-Type: ReDIF-Article 1.0 Author-Name: Ewa Strzalkowska-Kominiak Author-X-Name-First: Ewa Author-X-Name-Last: Strzalkowska-Kominiak Author-Name: Winfried Stute Author-X-Name-First: Winfried Author-X-Name-Last: Stute Title: The statistical analysis of consecutive survival data under serial dependence Abstract: In the analysis of medical data, one often encounters data that are observed sequentially over time. For example in AIDS studies, let X1 denote the time of infection, X2 the time when antibodies occur and X3 the time when AIDS is diagnosed for the first time. Typically, the variables of interest are the lifetimes U1=X2−X1 and U2=X3−X2, which may be dependent. While in applications, U1 is often truncated from the right, U2 may be censored due to time limitations. It is the aim of this paper to statistically analyse the joint distribution of the pair (U1, U2). Journal: Journal of Nonparametric Statistics Pages: 585-597 Issue: 5 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250902971740 File-URL: http://hdl.handle.net/10.1080/10485250902971740 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:5:p:585-597 Template-Type: ReDIF-Article 1.0 Author-Name: J. Barrientos-Marin Author-X-Name-First: J. Author-X-Name-Last: Barrientos-Marin Author-Name: F. Ferraty Author-X-Name-First: F. Author-X-Name-Last: Ferraty Author-Name: P. Vieu Author-X-Name-First: P. Author-X-Name-Last: Vieu Title: Locally modelled regression and functional data Abstract: The general framework of this paper deals with the nonparametric regression of a scalar response on a functional variable (i.e. one observation can be a curve, surface, or any other object lying into an infinite-dimensional space). This paper proposes to model local behaviour of the regression operator (i.e. the link between a scalar response and an explanatory functional variable). To this end, one introduces a functional approach in the same spirit as local linear ideas in nonparametric regression. The main advantage of this functional local method is to propose an explicit expression of a kernel-type estimator which makes its computation easy and fast while keeping good predictive performance. Asymptotic properties are stated, and a functional data set illustrates the good behaviour of this functional locally modelled regression method. Journal: Journal of Nonparametric Statistics Pages: 617-632 Issue: 5 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903089930 File-URL: http://hdl.handle.net/10.1080/10485250903089930 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:5:p:617-632 Template-Type: ReDIF-Article 1.0 Author-Name: Ya. Nikitin Author-X-Name-First: Ya. Author-X-Name-Last: Nikitin Title: Large deviations of U-empirical Kolmogorov–Smirnov tests and their efficiency Abstract: Non-degenerate U-empirical Kolmogorov–Smirnov tests are studied and their large deviation asymptotics under the null-hypothesis is described. Several examples of such statistics used for testing goodness-of-fit and symmetry are considered. It is shown how to calculate their local Bahadur efficiency. Journal: Journal of Nonparametric Statistics Pages: 649-668 Issue: 5 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903118085 File-URL: http://hdl.handle.net/10.1080/10485250903118085 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:5:p:649-668 Template-Type: ReDIF-Article 1.0 Author-Name: Elvan Ceyhan Author-X-Name-First: Elvan Author-X-Name-Last: Ceyhan Title: Directional clustering tests based on nearest neighbour contingency tables Abstract: Spatial interaction between two or more classes or species has important implications in various fields, and might cause multivariate patterns such as segregation or association. Segregation occurs when members of a class or species are more likely to be found near members of the same class or conspecifics; association occurs when members of a class or species are more likely to be found near members of another class or species. The null patterns considered are random labelling and complete spatial randomness (CSR) of points from two or more classes, which is henceforth called CSR independence. The clustering tests based on nearest neighbour contingency tables (NNCTs) that are in use in the literature are two-sided tests. In this article, we consider the directional (i.e. one-sided) versions of the cell-specific NNCT tests and introduce new directional NNCT tests for the two-class case. We analyse the distributional properties and compare the empirical significant levels and empirical power estimates of the tests using extensive Monte Carlo simulations. We demonstrate that the new directional tests have comparable performance with the currently available NNCT tests in terms of empirical size and power. We use an ecological data set for illustrative purposes and provide guidelines for using these NNCT tests. Journal: Journal of Nonparametric Statistics Pages: 599-616 Issue: 5 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903199861 File-URL: http://hdl.handle.net/10.1080/10485250903199861 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:5:p:599-616 Template-Type: ReDIF-Article 1.0 Author-Name: Bianca Teodorescu Author-X-Name-First: Bianca Author-X-Name-Last: Teodorescu Author-Name: Ingrid Van Keilegom Author-X-Name-First: Ingrid Author-X-Name-Last: Van Keilegom Title: A goodness-of-fit test for generalised conditional linear models under left truncation and right censoring Abstract: Consider a semiparametric time-varying coefficients regression model of the following form: φ(S(z|X))=β(z)t X, where φ is a known link function, S(·|X) is the survival function of a response Y; given a covariate X, X=(1, X, X2, …, Xp) and β(z)=(β0(z), …, βp(z))t is the unknown vector of regression coefficients. This model reduces for special choices of φ to, e.g. the additive hazards model or the Cox proportional hazards model with time-dependent coefficients. The response is subject to left truncation and right censoring. An omnibus goodness-of-fit test is developed to test whether the model fits the data. A bootstrap version, to approximate the critical values of the test, is proposed and proved to work from a practical point of view as well. The test is also applied to real data. Journal: Journal of Nonparametric Statistics Pages: 547-566 Issue: 5 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903302788 File-URL: http://hdl.handle.net/10.1080/10485250903302788 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:5:p:547-566 Template-Type: ReDIF-Article 1.0 Author-Name: Stefan Sperlich Author-X-Name-First: Stefan Author-X-Name-Last: Sperlich Author-Name: María José Lombardía Author-X-Name-First: María Author-X-Name-Last: José Lombardía Title: Local polynomial inference for small area statistics: estimation, validation and prediction Abstract: Small area statistics has received considerable attention in the last two decades from both public and private sectors. More recently, semiparametric mixed-effects models have been proposed for a more flexible modelling. Surprisingly, although model specification testing is of particular importance in small area statistics, this has been less explored. Its importance is based on the fact that small area statistics applies model-based estimation and prediction. Local polynomials can nest typically used parametric models without bias – independent of the smoothing parameter – and are therefore particularly useful in practice. First, estimation and testing with local polynomials is introduced for mixed-effects models. Several extensions for further structural modelling with dimension-reducing effects are discussed. Second, different computationally attractive specification tests are proposed and compared. The methods are compared along simulation studies. Its usefulness is underpinned by the small-area regression problems of forest stand and farm production. Journal: Journal of Nonparametric Statistics Pages: 633-648 Issue: 5 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903311607 File-URL: http://hdl.handle.net/10.1080/10485250903311607 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:5:p:633-648 Template-Type: ReDIF-Article 1.0 Author-Name: Carla Moreira Author-X-Name-First: Carla Author-X-Name-Last: Moreira Author-Name: Jacobo de Uña-Álvarez Author-X-Name-First: Jacobo Author-X-Name-Last: de Uña-Álvarez Title: Bootstrapping the NPMLE for doubly truncated data Abstract: Doubly truncated data appear in a number of applications, including astronomy and survival analysis. In this paper we review the existing methods to compute the nonparametric maximum likelihood estimator (NPMLE) under double truncation, which has no explicit form and must be approximated numerically. We introduce the bootstrap as a suitable method to estimate the finite sample distribution of the NPMLE under double truncation. The performance of the bootstrap is investigated in a simulation study. The nonstandard case in which the right- and left-truncation times determine each other is covered. As an illustration, nonparametric estimation and inference on the birth process and the age at diagnosis for childhood cancer in North Portugal is considered. Journal: Journal of Nonparametric Statistics Pages: 567-583 Issue: 5 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903556102 File-URL: http://hdl.handle.net/10.1080/10485250903556102 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:5:p:567-583 Template-Type: ReDIF-Article 1.0 Author-Name: Ricardo Cao Author-X-Name-First: Ricardo Author-X-Name-Last: Cao Author-Name: Winfried Stute Author-X-Name-First: Winfried Author-X-Name-Last: Stute Author-Name: Philippe Vieu Author-X-Name-First: Philippe Author-X-Name-Last: Vieu Author-Name: Jacobo de Uña Author-X-Name-First: Jacobo Author-X-Name-Last: de Uña Title: Editorial Journal: Pages: 545-546 Issue: 5 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903564858 File-URL: http://hdl.handle.net/10.1080/10485250903564858 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:5:p:545-546 Template-Type: ReDIF-Article 1.0 Author-Name: I. Rahimov Author-X-Name-First: I. Author-X-Name-Last: Rahimov Author-Name: M. Omar Author-X-Name-First: M. Author-X-Name-Last: Omar Title: Validity of the bootstrap in the critical process with a non-stationary immigration Abstract: In the critical branching process with a stationary immigration, the standard parametric bootstrap for an estimator of the offspring mean is invalid. We consider the process with non-stationary immigration, whose mean and variance α(n) and β(n) are finite for each n≥1 and are regularly varying sequences with non-negative exponents α and β, respectively. We prove that if α(n)→∞ and β (n)=o(nα2(n)) as n→∞, then the standard parametric bootstrap procedure leads to a valid approximation for the distribution of the conditional least-squares estimator in the sense of convergence in probability. Monte Carlo and bootstrap simulations for the process confirm the theoretical findings in the paper and highlight the validity and utility of the bootstrap as it mimics the Monte Carlo pivots even when generation size is small. Journal: Journal of Nonparametric Statistics Pages: 1-19 Issue: 1 Volume: 23 Year: 2011 X-DOI: 10.1080/10485250903085839 File-URL: http://hdl.handle.net/10.1080/10485250903085839 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:1-19 Template-Type: ReDIF-Article 1.0 Author-Name: Shujie Ma Author-X-Name-First: Shujie Author-X-Name-Last: Ma Author-Name: Lijian Yang Author-X-Name-First: Lijian Author-X-Name-Last: Yang Title: A jump-detecting procedure based on spline estimation Abstract: In a random-design nonparametric regression model, procedures for detecting jumps in the regression function via constant and linear spline estimation method are proposed based on the maximal differences of the spline estimators among neighbouring knots, the limiting distributions of which are obtained when the regression function is smooth. Simulation experiments provide strong evidence that corroborates with the asymptotic theory, while the computing is extremely fast. The detecting procedure is illustrated by analysing the thickness of pennies data set. Journal: Journal of Nonparametric Statistics Pages: 67-81 Issue: 1 Volume: 23 Year: 2011 X-DOI: 10.1080/10485250903571978 File-URL: http://hdl.handle.net/10.1080/10485250903571978 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:67-81 Template-Type: ReDIF-Article 1.0 Author-Name: Na Li Author-X-Name-First: Na Author-X-Name-Last: Li Author-Name: Xingzhong Xu Author-X-Name-First: Xingzhong Author-X-Name-Last: Xu Author-Name: Pei Jin Author-X-Name-First: Pei Author-X-Name-Last: Jin Title: Testing the linearity in partially linear models Abstract: A test is proposed to check the linearity of the nonparametric portion in the partially linear regression model with a linear interpolation. The test is given by a p-value which is derived using the fiducial method. This p-value can also be thought as a generalised p-value. Under the null hypothesis, the p-value is uniformly distributed on interval (0, 1). Meanwhile the test is consistent under mild conditions. Finally, a good finite sample performance of the test is investigated by simulations, in which comparisons with other tests are also given. Journal: Journal of Nonparametric Statistics Pages: 99-114 Issue: 1 Volume: 23 Year: 2011 X-DOI: 10.1080/10485251003615574 File-URL: http://hdl.handle.net/10.1080/10485251003615574 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:99-114 Template-Type: ReDIF-Article 1.0 Author-Name: Yoichi Nishiyama Author-X-Name-First: Yoichi Author-X-Name-Last: Nishiyama Title: Impossibility of weak convergence of kernel density estimators to a non-degenerate law in (ℝ) Abstract: It is well known that the kernel estimator for the probability density f on ℝd has pointwise asymptotic normality and that its weak convergence in a function space, especially with the uniform topology, is a difficult problem. One may conjecture that the weak convergence in L2(ℝd) could be possible. In this paper, we deny this conjecture. That is, letting , we prove that for any sequence {rn} of positive constants such that rn=o(√n), if the rescaled residual rn([fcirc]n−fn) converges weakly to a Borel limit in L2(ℝd), then the limit is necessarily degenerate. Journal: Journal of Nonparametric Statistics Pages: 129-135 Issue: 1 Volume: 23 Year: 2011 X-DOI: 10.1080/10485251003678507 File-URL: http://hdl.handle.net/10.1080/10485251003678507 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:129-135 Template-Type: ReDIF-Article 1.0 Author-Name: Jaehee Kim Author-X-Name-First: Jaehee Author-X-Name-Last: Kim Author-Name: Jeffrey Hart Author-X-Name-First: Jeffrey Author-X-Name-Last: Hart Title: A change-point estimator using local Fourier series Abstract: In this paper, we propose a change-point estimator based on local Fourier series estimates. At each potential change point, two Fourier series estimates are computed, one using data to the left of the possible change point and the other using data to the right. The difference between these estimates is computed, and the change-point estimate is defined to be the point at which this absolute difference is maximised. Mean-squared error properties of our local series estimates are derived and the change-point estimator is shown to converege to the truth at rate n−1 (where n is the sample size). In a simulation study, the proposed change-point estimator has a better overall performance than a local linear method. A data-driven bandwidth selector is also proposed and applied to the classical Nile River data. Journal: Journal of Nonparametric Statistics Pages: 83-98 Issue: 1 Volume: 23 Year: 2011 X-DOI: 10.1080/10485251003721232 File-URL: http://hdl.handle.net/10.1080/10485251003721232 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:83-98 Template-Type: ReDIF-Article 1.0 Author-Name: Lawrence Brown Author-X-Name-First: Lawrence Author-X-Name-Last: Brown Author-Name: Xin Fu Author-X-Name-First: Xin Author-X-Name-Last: Fu Author-Name: Linda Zhao Author-X-Name-First: Linda Author-X-Name-Last: Zhao Title: Confidence intervals for nonparametric regression Abstract: In nonparametric function estimation, providing a confidence interval with the right coverage is a challenging problem. This is especially the case when the underlying function has a wide range of unknown degrees of smoothness. Here, we propose two methods of constructing an average coverage confidence interval built from block shrinkage estimation methods. One is based on the James–Stein shrinkage estimator; the other begins with a Bayesian perspective and is based on a modification of the harmonic prior estimator. Simulation shows that these confidence intervals have average coverage close to or above the nominal coverage even when the underlying function is rough and/or the signal-to-noise ratio is small. Both of the confidence intervals perform consistently well across all the investigated test functions even though these functions have very different shapes and smoothness. Journal: Journal of Nonparametric Statistics Pages: 149-163 Issue: 1 Volume: 23 Year: 2011 X-DOI: 10.1080/10485251003753201 File-URL: http://hdl.handle.net/10.1080/10485251003753201 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:149-163 Template-Type: ReDIF-Article 1.0 Author-Name: Taeryon Choi Author-X-Name-First: Taeryon Author-X-Name-Last: Choi Author-Name: Jian Shi Author-X-Name-First: Jian Author-X-Name-Last: Shi Author-Name: Bo Wang Author-X-Name-First: Bo Author-X-Name-Last: Wang Title: A Gaussian process regression approach to a single-index model Abstract: We consider a Gaussian process regression (GPR) approach to analysing a single-index model (SIM) from the Bayesian perspective. Specifically, the unknown link function is assumed to be a Gaussian process a priori and a prior on the index vector is considered based on a simple uniform distribution on the unit sphere. The posterior distributions for the unknown parameters are derived, and the posterior inference of the proposed approach is performed via Markov chain Monte Carlo methods based on them. Particularly, in estimating the hyperparameters, different numerical schemes are implemented: fully Bayesian methods and empirical Bayes methods. Numerical illustration of the proposed approach is also made using simulation data as well as well-known real data. The proposed approach broadens the scope of the applicability of the SIM as well as the GPR. In addition, we discuss the theoretical aspect of the proposed method in terms of posterior consistency. Journal: Journal of Nonparametric Statistics Pages: 21-36 Issue: 1 Volume: 23 Year: 2011 X-DOI: 10.1080/10485251003768019 File-URL: http://hdl.handle.net/10.1080/10485251003768019 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:21-36 Template-Type: ReDIF-Article 1.0 Author-Name: Max de Lima Author-X-Name-First: Max Author-X-Name-Last: de Lima Author-Name: Gregorio Atuncar Author-X-Name-First: Gregorio Author-X-Name-Last: Atuncar Title: A Bayesian method to estimate the optimal bandwidth for multivariate kernel estimator Abstract: The estimation of multivariate densities using the kernel method has wide applicability. However, this problem has received less attention than the univariate case. This is mainly due to the increasing difficulty in estimating the optimal smoothing matrix, especially when the components are correlated. To overcome this difficulty, we propose in this work a Bayesian method to estimate the optimal smoothing matrix H. A loss function is defined and the estimator of H is the matrix minimising the loss function. We carried out simulations with a mixture of multivariate densities with correlation and the results were highly satisfactory. Journal: Journal of Nonparametric Statistics Pages: 137-148 Issue: 1 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.485200 File-URL: http://hdl.handle.net/10.1080/10485252.2010.485200 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:137-148 Template-Type: ReDIF-Article 1.0 Author-Name: Xiaoqin Li Author-X-Name-First: Xiaoqin Author-X-Name-Last: Li Author-Name: Wenzhi Yang Author-X-Name-First: Wenzhi Author-X-Name-Last: Yang Author-Name: Shuhe Hu Author-X-Name-First: Shuhe Author-X-Name-Last: Hu Author-Name: Xuejun Wang Author-X-Name-First: Xuejun Author-X-Name-Last: Wang Title: The Bahadur representation for sample quantile under NOD sequence Abstract: In this paper, we investigate the Bahadur representation of sample quantile based on negatively orthant dependent sequence, which is weaker than negatively associated sequence. Our results extend and improve the results of Ling [(2008), ‘The Bahadur Representation for Sample Quantiles Under Negatively Associated Sequence’, Statistics & Probability Letters, 78, 2660–2663]. Journal: Journal of Nonparametric Statistics Pages: 59-65 Issue: 1 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.486033 File-URL: http://hdl.handle.net/10.1080/10485252.2010.486033 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:59-65 Template-Type: ReDIF-Article 1.0 Author-Name: R. Girard Author-X-Name-First: R. Author-X-Name-Last: Girard Title: Fast rate of convergence in high-dimensional linear discriminant analysis Abstract: This paper gives a theoretical analysis of high-dimensional linear discrimination of Gaussian data. We study the excess risk of linear discriminant rules. We emphasis the poor performances of standard procedures in the case when dimension p is larger than sample size n. The corresponding theoretical results are non-asymptotic lower bounds. On the other hand, we propose two discrimination procedures based on dimensionality reduction and provide associated rates of convergence which can be O(log(p)/n) under sparsity assumptions. Finally, all our results rely on a theorem that provides simple sharp relations between the excess risk and an estimation error associated with the geometric parameters defining the used discrimination rule. Journal: Journal of Nonparametric Statistics Pages: 165-183 Issue: 1 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.487531 File-URL: http://hdl.handle.net/10.1080/10485252.2010.487531 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:165-183 Template-Type: ReDIF-Article 1.0 Author-Name: Yichao Wu Author-X-Name-First: Yichao Author-X-Name-Last: Wu Title: An ordinary differential equation-based solution path algorithm Abstract: Efron, Hastie, Johnstone, and Tibshirani [(2004), ‘Least Angle Regression (with discussions)’, The Annals of Statistics, 32, 409–499] proposed least angle regression (LAR), a solution path algorithm for the least squares regression. They pointed out that a slight modification of the LAR gives the LASSO [Tibshirani, R. (1996), ‘Regression Shrinkage and Selection Via the Lasso’, Journal of the Royal Statistical Society, Series B, 58, 267–288] solution path. However, it is largely unknown how to extend this solution path algorithm to models beyond the least squares regression. In this work, we propose an extension of the LAR for generalised linear models and the quasi-likelihood model by showing that the corresponding solution path is piecewise given by solutions of ordinary differential equation (ODE) systems. Our contribution is twofold. First, we provide a theoretical understanding on how the corresponding solution path propagates. Second, we propose an ODE-based algorithm to obtain the whole solution path. Journal: Journal of Nonparametric Statistics Pages: 185-199 Issue: 1 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.490584 File-URL: http://hdl.handle.net/10.1080/10485252.2010.490584 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:185-199 Template-Type: ReDIF-Article 1.0 Author-Name: Tracy Wu Author-X-Name-First: Tracy Author-X-Name-Last: Wu Author-Name: Haiqun Lin Author-X-Name-First: Haiqun Author-X-Name-Last: Lin Author-Name: Yan Yu Author-X-Name-First: Yan Author-X-Name-Last: Yu Title: Single-index coefficient models for nonlinear time series Abstract: The single-index coefficient model, where the coefficients are functions of an index of a covariate vector, is a powerful tool for modelling nonlinearity in multivariate estimation. By reducing the covariate vector to an index which is usually a linear combination of covariates, the single-index coefficient model overcomes the well-known phenomenon of ‘curse-of-dimensionality’. We estimate the univariate varying coefficients with penalised splines (PS). An iterative data-driven algorithm is developed, adaptively selecting the index. The algorithm is based on the observation that given an estimated index, the varying-coefficient model using PS is essentially a linear ridge regression with spline bases. Our experiments show that the proposed algorithm gives rapid convergence. We also establish large sample properties assuming fixed number of knots. The usual jointly stationary assumption for dependent data is relaxed with weaker size requirements for either φ-mixing or α-mixing. Finally, we present an application to a gross national product data set and a simulated example. Journal: Journal of Nonparametric Statistics Pages: 37-58 Issue: 1 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.497554 File-URL: http://hdl.handle.net/10.1080/10485252.2010.497554 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:37-58 Template-Type: ReDIF-Article 1.0 Author-Name: Heng Lian Author-X-Name-First: Heng Author-X-Name-Last: Lian Title: Functional partial linear model Abstract: When predicting scalar responses in the situation where the explanatory variables are functions, it is sometimes the case that some functional variables are related to responses linearly while other variables have more complicated relationships with the responses. In this paper, we propose a new semi-parametric model to take advantage of both parametric and nonparametric functional modelling. Asymptotic properties of the proposed estimators are established and finite sample behaviour is investigated through a small simulation experiment. Journal: Journal of Nonparametric Statistics Pages: 115-128 Issue: 1 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.500385 File-URL: http://hdl.handle.net/10.1080/10485252.2010.500385 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:115-128 Template-Type: ReDIF-Article 1.0 Author-Name: Rossita Yunus Author-X-Name-First: Rossita Author-X-Name-Last: Yunus Author-Name: Shahjahan Khan Author-X-Name-First: Shahjahan Author-X-Name-Last: Khan Title: M-tests for multivariate regression model Abstract: The M-estimation method is used to define the unrestricted test, restricted test and pre-test test (PTT) for testing the intercept vector of a multivariate simple regression model when it is a priori suspected that the slope vector has some specified values. The asymptotic distribution of the test statistics and the asymptotic power functions of the proposed M-tests are derived. Performances of the M-tests are compared both analytically and graphically. The analytical results as well as an illustrative simulation study to compare the size and power of the M-tests reveal a reasonable dominance of the PTT over the other two tests. Journal: Journal of Nonparametric Statistics Pages: 201-218 Issue: 1 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.503896 File-URL: http://hdl.handle.net/10.1080/10485252.2010.503896 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:201-218 Template-Type: ReDIF-Article 1.0 Author-Name: Jun Han Author-X-Name-First: Jun Author-X-Name-Last: Han Title: Distribution-free estimators of variance components for multivariate linear mixed models Abstract: Non-iterative, distribution-free, and unbiased estimators of variance components including minimum norm quadratic unbiased estimators and the method of moments estimators are derived for multivariate linear mixed models. A general inter-cluster variance matrix, a same-member only general inter-response variance matrix, and an uncorrelated intra-cluster error structure for each response are assumed. Some properties of the proposed estimators such as unbiasedness and existence are discussed, and related computational issues are addressed. A simulation study is conducted to compare the proposed estimators with Gaussian (restricted) maximum likelihood estimators in terms of bias and mean square error. An application of gene expression family study is presented to illustrate the proposed estimators. Journal: Journal of Nonparametric Statistics Pages: 219-235 Issue: 1 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.507868 File-URL: http://hdl.handle.net/10.1080/10485252.2010.507868 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:219-235 Template-Type: ReDIF-Article 1.0 Author-Name: Colin Wu Author-X-Name-First: Colin Author-X-Name-Last: Wu Author-Name: Xin Tian Author-X-Name-First: Xin Author-X-Name-Last: Tian Author-Name: Jarvis Yu Author-X-Name-First: Jarvis Author-X-Name-Last: Yu Title: Nonparametric estimation for time-varying transformation models with longitudinal data Abstract: Regression methods for longitudinal analyses have traditionally focused on conditional-mean-based models. In many situations, the relevant scientific questions could be better studied by modelling the conditional distributions of the outcome variables as a function of time and other covariates. In this paper, we propose a class of time-varying transformation models for modelling the cumulative distribution function of a response variable conditioning on a set of covariates, and develop a two-step smoothing method for estimating the time-varying parameters. Applications and finite sample properties of our models and smoothing estimators are demonstrated through a cohort study of childhood obesity and cardiovascular risk factors, and a simulation study. Theoretical properties are developed for the two-step local polynomial estimators. Our approach provides a useful statistical tool in longitudinal analysis when the conditional-mean-based methods are inappropriate. Journal: Journal of Nonparametric Statistics Pages: 133-147 Issue: 2 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903160988 File-URL: http://hdl.handle.net/10.1080/10485250903160988 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:2:p:133-147 Template-Type: ReDIF-Article 1.0 Author-Name: Haiyan Wang Author-X-Name-First: Haiyan Author-X-Name-Last: Wang Author-Name: Michael Akritas Author-X-Name-First: Michael Author-X-Name-Last: Akritas Title: Inference from heteroscedastic functional data Abstract: Technological advancements have produced an abundance of data sets in which a large number of repeated measurements are observed within a subject or stratum. Many of these data sets are based on a small number of subjects rendering most existing inferential methods unsuitable. This paper develops test procedures based on a novel model for nested heteroscedastic high-dimensional data which we propose. The novelty of the model rests on the fact that the random effects are assumed to be neither uncorrelated nor normal. The model is nonparametric in the sense that it leaves the covariance structure unspecified and applies to both discrete and continuous data. The test procedures developed are useful for evaluating the effects of time as well as their interactions with the crossed factors on the stratum. The asymptotic theory of the test statistics is driven by a large number of measurements per subject and the assumption of nonstationary α-mixing on the error term. Simulation studies and real applications show that the proposed tests are more powerful in detecting effects compared with benchmark methods in data with very limited number of replications. Journal: Journal of Nonparametric Statistics Pages: 149-168 Issue: 2 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903171621 File-URL: http://hdl.handle.net/10.1080/10485250903171621 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:2:p:149-168 Template-Type: ReDIF-Article 1.0 Author-Name: Tae Kim Author-X-Name-First: Tae Author-X-Name-Last: Kim Author-Name: Jeong Park Author-X-Name-First: Jeong Author-X-Name-Last: Park Author-Name: Gyu Song Author-X-Name-First: Gyu Author-X-Name-Last: Song Title: An asymptotic theory for the nugget estimator in spatial models Abstract: The nugget effect is an important parameter for spatial prediction. In this paper, we propose a nonparametric nugget estimator based on the classical semivariogram estimator and describe its large sample distributional properties. Our main results are a central limit theorem and a risk calculation for the estimator when observations are made from a nearly infill domain sampling. From our results, we note that the performance of the estimator depends on the sampling design as well as the choice of bandwidth. In particular, we show that the estimator suffers from strong dependency when d, the dimension of the underlying spatial process, is less than or equal to 2a, a parameter related to the degree of smoothness and dependence of the underlying process. When d>2a, however, the estimator turns out to achieve an optimal rate with an optimal choice of h. We report on the results of simulations to empirically study the estimator. Journal: Journal of Nonparametric Statistics Pages: 181-195 Issue: 2 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903193997 File-URL: http://hdl.handle.net/10.1080/10485250903193997 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:2:p:181-195 Template-Type: ReDIF-Article 1.0 Author-Name: Jesse Frey Author-X-Name-First: Jesse Author-X-Name-Last: Frey Title: Data-driven nonparametric tolerance sets Abstract: We develop two new nonstandard methods for obtaining nonparametric tolerance sets from a univariate simple random sample. The first method consists of taking the union of a certain number of the intervals between the order statistics from the sample. The second method, which generalises the first, consists of taking the union of a certain number of the intervals between a prespecified subset of the order statistics from the sample. For each method, the number of intervals to choose is determined by the coverage probability properties desired. Both methods allow the choice of intervals to be made arbitrarily and after seeing the data, but minimal length may be used as a choice criterion. We show how to find the exact coverage probability for sets obtained using either method, and we explore some properties of sets obtained using the two methods. We use an ecological data set and a simulation study to show that the small-sample performance of the two methods compares favourably with that of other nonparametric tolerance set methods in the literature. Journal: Journal of Nonparametric Statistics Pages: 169-180 Issue: 2 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903248668 File-URL: http://hdl.handle.net/10.1080/10485250903248668 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:2:p:169-180 Template-Type: ReDIF-Article 1.0 Author-Name: Kairat Mynbaev Author-X-Name-First: Kairat Author-X-Name-Last: Mynbaev Author-Name: Carlos Martins-Filho Author-X-Name-First: Carlos Author-X-Name-Last: Martins-Filho Title: Bias reduction in kernel density estimation via Lipschitz condition Abstract: In this paper we propose a new nonparametric kernel-based estimator for a density function f which achieves bias reduction relative to the classical Rosenblatt–Parzen estimator. Contrary to some existing estimators that provide for bias reduction, our estimator has a full asymptotic characterisation including uniform consistency and asymptotic normality. In addition, we show that bias reduction can be achieved without the disadvantage of potential negativity of the estimated density – a deficiency that results from using higher order kernels. Our results are based on imposing global Lipschitz conditions on f and defining a novel corresponding kernel. A Monte Carlo study is provided to illustrate the estimator's finite sample performance. Journal: Journal of Nonparametric Statistics Pages: 219-235 Issue: 2 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903266058 File-URL: http://hdl.handle.net/10.1080/10485250903266058 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:2:p:219-235 Template-Type: ReDIF-Article 1.0 Author-Name: Tang Qingguo Author-X-Name-First: Tang Author-X-Name-Last: Qingguo Author-Name: Cheng Longsheng Author-X-Name-First: Cheng Author-X-Name-Last: Longsheng Title: B-spline estimation for spatial data Abstract: Data collected on the surface of the earth often have spatial interaction. In this paper, a global smoothing procedure is developed using a tensor product of B-spline function approximations for estimating the spatial multi-dimensional conditional regression function. Under mild regularity assumptions, the global convergence rates of the B-spline estimators are established. Asymptotic results show that our B-spline estimators achieve the optimal convergence rate. The asymptotic normality of our estimator is also derived. Finite sample properties of our procedures are studied through Monte Carlo simulations. Journal: Journal of Nonparametric Statistics Pages: 197-217 Issue: 2 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903272569 File-URL: http://hdl.handle.net/10.1080/10485250903272569 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:2:p:197-217 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Martin Author-X-Name-First: Michael Author-X-Name-Last: Martin Author-Name: Steven Roberts Author-X-Name-First: Steven Author-X-Name-Last: Roberts Title: Jackknife-after-bootstrap regression influence diagnostics Abstract: We propose a bootstrap approach to gauging the size of regression influence measures. The bootstrap cut-offs generated are based on approximating the sampling distribution of the respective measures under resampling, work well for small samples, and allow for features such as asymmetric cut-offs. The bootstrap method uses Efron's jackknife-after-bootstrap idea to deal with the issue of an influential point contaminating the resamples from which cut-offs are calculated. The method is illustrated through both real-world examples and a simulation study, the results of which suggest that the bootstrap method provides a reliable alternative to traditional methods particularly in small to moderate samples. Journal: Journal of Nonparametric Statistics Pages: 257-269 Issue: 2 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903287906 File-URL: http://hdl.handle.net/10.1080/10485250903287906 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:2:p:257-269 Template-Type: ReDIF-Article 1.0 Author-Name: Jien Chen Author-X-Name-First: Jien Author-X-Name-Last: Chen Author-Name: Nicole Lazar Author-X-Name-First: Nicole Author-X-Name-Last: Lazar Title: Quantile estimation for discrete data via empirical likelihood Abstract: Quantile estimation for discrete distributions has not been well studied, although discrete data are common in practice. Under the assumption that data are drawn from a discrete distribution, we examine the consistency of the maximum empirical likelihood estimator (MELE) of the pth population quantile θp, with the assistance of a jittering method and results for continuous distributions. The MELE may or may not be consistent for θp, depending on whether or not the underlying distribution has a plateau at the level of p. We propose an empirical likelihood-based categorisation procedure which not only helps in determining the shape of the true distribution at level p but also provides a way of formulating a new estimator that is consistent in any case. Analogous to confidence intervals in the continuous case, the probability of a correct estimate (PCE) accompanies the point estimator. Simulation results show that PCE can be estimated using a simple bootstrap method. Journal: Journal of Nonparametric Statistics Pages: 237-255 Issue: 2 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903301525 File-URL: http://hdl.handle.net/10.1080/10485250903301525 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:2:p:237-255 Template-Type: ReDIF-Article 1.0 Author-Name: Hsin-wen Chang Author-X-Name-First: Hsin-wen Author-X-Name-Last: Chang Author-Name: Hammou El Barmi Author-X-Name-First: Hammou Author-X-Name-Last: El Barmi Author-Name: Ian W. McKeague Author-X-Name-First: Ian W. Author-X-Name-Last: McKeague Title: Tests for stochastic ordering under biased sampling Abstract: In two-sample comparison problems it is often of interest to examine whether one distribution function majorises the other, that is, for the presence of stochastic ordering. This paper develops a nonparametric test for stochastic ordering from size-biased data, allowing the pattern of the size bias to differ between the two samples. The test is formulated in terms of a maximally selected local empirical likelihood statistic. A Gaussian multiplier bootstrap is devised to calibrate the test. Simulation results show that the proposed test outperforms an analogous Wald-type test, and that it provides substantially greater power over ignoring the size bias. The approach is illustrated using data on blood alcohol concentration of drivers involved in car accidents, where the size bias is due to drunker drivers being more likely to be involved in accidents. Further, younger drivers tend to be more affected by alcohol, so in making comparisons with older drivers the analysis is adjusted for differences in the patterns of size bias. Journal: Journal of Nonparametric Statistics Pages: 659-682 Issue: 4 Volume: 28 Year: 2016 Month: 10 X-DOI: 10.1080/10485252.2016.1225048 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1225048 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:4:p:659-682 Template-Type: ReDIF-Article 1.0 Author-Name: Xiaotian Zhu Author-X-Name-First: Xiaotian Author-X-Name-Last: Zhu Author-Name: David R. Hunter Author-X-Name-First: David R. Author-X-Name-Last: Hunter Title: Theoretical grounding for estimation in conditional independence multivariate finite mixture models Abstract: For the nonparametric estimation of multivariate finite mixture models with the conditional independence assumption, we propose a new formulation of the objective function in terms of penalised smoothed Kullback–Leibler distance. The nonlinearly smoothed majorisation-minimisation (NSMM) algorithm is derived from this perspective. An elegant representation of the NSMM algorithm is obtained using a novel projection-multiplication operator, a more precise monotonicity property of the algorithm is discovered, and the existence of a solution to the main optimisation problem is proved for the first time. Journal: Journal of Nonparametric Statistics Pages: 683-701 Issue: 4 Volume: 28 Year: 2016 Month: 10 X-DOI: 10.1080/10485252.2016.1225049 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1225049 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:4:p:683-701 Template-Type: ReDIF-Article 1.0 Author-Name: Aiting Shen Author-X-Name-First: Aiting Author-X-Name-Last: Shen Title: Complete convergence for weighted sums of END random variables and its application to nonparametric regression models Abstract: In this article, the complete convergence for weighted sums of extended negatively dependent (END, for short) random variables is investigated. Some sufficient conditions for the complete convergence are provided. In addition, the Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of END random variables is obtained. The results obtained in the article generalise and improve the corresponding one of Wang et al. [(2014b), ‘On Complete Convergence for an Extended Negatively Dependent Sequence’, Communications in Statistics-Theory and Methods, 43, 2923–2937]. As an application, the complete consistency for the estimator of nonparametric regression model is established. Journal: Journal of Nonparametric Statistics Pages: 702-715 Issue: 4 Volume: 28 Year: 2016 Month: 10 X-DOI: 10.1080/10485252.2016.1225050 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1225050 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:4:p:702-715 Template-Type: ReDIF-Article 1.0 Author-Name: Edsel A. Peña Author-X-Name-First: Edsel A. Author-X-Name-Last: Peña Title: Asymptotics for a class of dynamic recurrent event models Abstract: Asymptotic properties, both consistency and weak convergence, of estimators arising in a general class of dynamic recurrent event models are presented. The class of models take into account the impact of interventions after each event occurrence, the impact of accumulating event occurrences, the induced informative and dependent right-censoring mechanism due to the data-accrual scheme, and the effect of covariate processes on the recurrent event occurrences. The class of models subsumes as special cases many of the recurrent event models that have been considered in biostatistics, reliability, and in the social sciences. The asymptotic properties presented have the potential of being useful in developing goodness-of-fit and model validation procedures, confidence intervals and confidence bands constructions, and hypothesis testing procedures for the finite- and infinite-dimensional parameters of a general class of dynamic recurrent event models, albeit the models without frailties. Journal: Journal of Nonparametric Statistics Pages: 716-735 Issue: 4 Volume: 28 Year: 2016 Month: 10 X-DOI: 10.1080/10485252.2016.1225733 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1225733 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:4:p:716-735 Template-Type: ReDIF-Article 1.0 Author-Name: Hongsheng Dai Author-X-Name-First: Hongsheng Author-X-Name-Last: Dai Author-Name: Marialuisa Restaino Author-X-Name-First: Marialuisa Author-X-Name-Last: Restaino Author-Name: Huan Wang Author-X-Name-First: Huan Author-X-Name-Last: Wang Title: A class of nonparametric bivariate survival function estimators for randomly censored and truncated data Abstract: This paper proposes a class of nonparametric estimators for the bivariate survival function estimation under both random truncation and random censoring. In practice, the pair of random variables under consideration may have certain parametric relationship. The proposed class of nonparametric estimators uses such parametric information via a data transformation approach and thus provides more accurate estimates than existing methods without using such information. The large sample properties of the new class of estimators and a general guidance of how to find a good data transformation are given. The proposed method is also justified via a simulation study and an application on an economic data set. Journal: Journal of Nonparametric Statistics Pages: 736-751 Issue: 4 Volume: 28 Year: 2016 Month: 10 X-DOI: 10.1080/10485252.2016.1225734 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1225734 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:4:p:736-751 Template-Type: ReDIF-Article 1.0 Author-Name: Seonjin Kim Author-X-Name-First: Seonjin Author-X-Name-Last: Kim Author-Name: Adriano Z. Zambom Author-X-Name-First: Adriano Z. Author-X-Name-Last: Zambom Title: A nonparametric hypothesis test for heteroscedasticity Abstract: In this paper, a hypothesis test for heteroscedasticity is proposed in a nonparametric regression model. The test statistic, which uses the residuals from a nonparametric fit of the mean function, is based on an adaptation of the well-known Levene's test. Using the recent theory for analysis of variance when the number of factor levels goes to infinity, the asymptotic distribution of the test statistic is established under the null hypothesis of homocedasticity and under local alternatives. Simulations suggest that the proposed test performs well in several situations, especially when the variance is a nonlinear function of the predictor. Journal: Journal of Nonparametric Statistics Pages: 752-767 Issue: 4 Volume: 28 Year: 2016 Month: 10 X-DOI: 10.1080/10485252.2016.1225735 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1225735 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:4:p:752-767 Template-Type: ReDIF-Article 1.0 Author-Name: F. Comte Author-X-Name-First: F. Author-X-Name-Last: Comte Author-Name: C. Dion Author-X-Name-First: C. Author-X-Name-Last: Dion Title: Nonparametric estimation in a multiplicative censoring model with symmetric noise Abstract: We consider the model $ Y_i=X_iU_i $ Yi=XiUi, $ i=1, \ldots , n $ i=1,…,n, where the $ X_i $ Xi, the $ U_i $ Ui and thus the $ Y_i $ Yi are all independent and identically distributed. The $ X_i $ Xi's have density f and are the variables of interest, the $ U_i $ Ui's are multiplicative noise with uniform density on $ [1-a,1+a] $ [1−a,1+a], for some 0<a<1, and the two sequences are independent. However, only the $ Y_i $ Yi's are observed. We study nonparametric estimation of both the density f and the corresponding survival function. In each context, a projection estimator of an auxiliary function is built, from which estimator of the function of interest is deduced. Risk bounds in term of integrated squared error are provided, showing that the dimension parameter associated with the projection step has to perform a compromise. Thus, a model selection strategy is proposed in both cases of density and survival function estimation. The resulting estimators are proven to reach the best possible risk bounds. Simulation experiments illustrate the good performances of the estimators and a real data example is described. Journal: Journal of Nonparametric Statistics Pages: 768-801 Issue: 4 Volume: 28 Year: 2016 Month: 10 X-DOI: 10.1080/10485252.2016.1225737 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1225737 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:4:p:768-801 Template-Type: ReDIF-Article 1.0 Author-Name: Qiqing Yu Author-X-Name-First: Qiqing Author-X-Name-Last: Yu Author-Name: Yuting Hsu Author-X-Name-First: Yuting Author-X-Name-Last: Hsu Title: Asymptotic normality of the product-limit-estimator Abstract: Under the standard right-censorship (RC) model, which assumes that the survival time and censoring time are independent, several sufficient conditions have been established for the product-limit estimator (PLE) being asymptotically normally distributed on the whole real line [see, e.g. Stute, W. (1995), ‘The central limit theorem under random censorship’, Ann. Statist., 23, 422–439]. However, it remains a difficult open problem what the necessary and sufficient conditions that the PLE has an asymptotic normality property on the whole real line is. In this paper, we settle the problem under both the standard RC model which assumes $ T\perp R $ T⊥R and the dependent RC model. Journal: Journal of Nonparametric Statistics Pages: 802-812 Issue: 4 Volume: 28 Year: 2016 Month: 10 X-DOI: 10.1080/10485252.2016.1225738 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1225738 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:4:p:802-812 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Corrigendum Journal: Journal of Nonparametric Statistics Pages: 875-877 Issue: 4 Volume: 28 Year: 2016 Month: 10 X-DOI: 10.1080/10485252.2016.1230269 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1230269 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:4:p:875-877 Template-Type: ReDIF-Article 1.0 Author-Name: Dehan Kong Author-X-Name-First: Dehan Author-X-Name-Last: Kong Author-Name: Ana-Maria Staicu Author-X-Name-First: Ana-Maria Author-X-Name-Last: Staicu Author-Name: Arnab Maity Author-X-Name-First: Arnab Author-X-Name-Last: Maity Title: Classical testing in functional linear models Abstract: We extend four tests common in classical regression – Wald, score, likelihood ratio and F tests – to functional linear regression, for testing the null hypothesis, that there is no association between a scalar response and a functional covariate. Using functional principal component analysis, we re-express the functional linear model as a standard linear model, where the effect of the functional covariate can be approximated by a finite linear combination of the functional principal component scores. In this setting, we consider application of the four traditional tests. The proposed testing procedures are investigated theoretically for densely observed functional covariates when the number of principal components diverges. Using the theoretical distribution of the tests under the alternative hypothesis, we develop a procedure for sample size calculation in the context of functional linear regression. The four tests are further compared numerically for both densely and sparsely observed noisy functional data in simulation experiments and using two real data applications. Journal: Journal of Nonparametric Statistics Pages: 813-838 Issue: 4 Volume: 28 Year: 2016 Month: 10 X-DOI: 10.1080/10485252.2016.1231806 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1231806 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:4:p:813-838 Template-Type: ReDIF-Article 1.0 Author-Name: G. Aneiros Author-X-Name-First: G. Author-X-Name-Last: Aneiros Author-Name: P. Vieu Author-X-Name-First: P. Author-X-Name-Last: Vieu Title: Sparse nonparametric model for regression with functional covariate Abstract: This paper proposes a fully nonparametric model for regression problems involving an infinite-dimensional covariate in which sparsity is modelled in an additive way. The continuous nature of the variable allows to develop new variable selection procedures. Theoretical results show the improvement, in terms of both rate of convergence and number $ p_n $ pn of predictor variables in the model, that one can get from these approaches. An application to some real curves data set is finally presented, which illustrates the double practical interest of the method: good predictive behaviour and interpretability of the outputs as points of the curves being of most impact. Journal: Journal of Nonparametric Statistics Pages: 839-859 Issue: 4 Volume: 28 Year: 2016 Month: 10 X-DOI: 10.1080/10485252.2016.1234050 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1234050 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:4:p:839-859 Template-Type: ReDIF-Article 1.0 Author-Name: Menggang Yu Author-X-Name-First: Menggang Author-X-Name-Last: Yu Title: Improving estimation efficiency for semi-competing risks data with partially observed terminal event Abstract: Semi-competing risks data arise when two types of events, non-terminal and terminal, may be observed. When the terminal event occurs first, it censors the non-terminal event. Otherwise the terminal event is observable after the occurrence of the non-terminal event. In practice, it can be hard to ascertain all terminal event information after the non-terminal event. Yu and Yiannoutsos [(2015), ‘Marginal and Conditional Distribution Estimation from Double-Sampled Semi-Competing Risks Data’, Scandinavian Journal of Statistics, 42, 87–103] considered a setting when the terminal event is ascertained via double sampling from only a subset of patients who experienced the non-terminal event. They discussed estimation for marginal and conditional distributions under this double sampled semi-competing risk data framework. We propose a more efficient estimation method in the same setting by fully utilising the non-terminal event information. The efficiency gain can be substantial as observed in our simulation study. Journal: Journal of Nonparametric Statistics Pages: 860-874 Issue: 4 Volume: 28 Year: 2016 Month: 10 X-DOI: 10.1080/10485252.2016.1234051 File-URL: http://hdl.handle.net/10.1080/10485252.2016.1234051 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:28:y:2016:i:4:p:860-874 Template-Type: ReDIF-Article 1.0 Author-Name: Lu Lin Author-X-Name-First: Lu Author-X-Name-Last: Lin Author-Name: Feng Li Author-X-Name-First: Feng Author-X-Name-Last: Li Title: Stable and bias-corrected estimation for nonparametric regression models Abstract: It is well known that in nonparametric regression setting, the common kernel estimators are sensitive to bandwidth and can not achieve a satisfactory convergence rate, especially for multivariate cases. To improve nonparametric estimation in the sense of both selection of bandwidth and convergence rate, this paper proposes a two-stage (or three-stage) regression estimation by combining nonparametric regression with parametric regression. The optimal design conditions, including the optimal bandwidth, are obtained. The newly proposed estimator has a simple structure and can achieve a smaller mean square error without use of the higher order kernel. Even if the prior selections of nonparametric estimation are not optimal (i.e. the smooth parameter is not optimally chosen), the new two-stage estimator still has a satisfactory convergence rate. This means that the newly proposed estimator is robust to the selection of bandwidth and then is a practical method. This new method is also suitable for general nonparametric regression models regardless of the dimension of explanatory variable and the structure assumption on regression function. Journal: Journal of Nonparametric Statistics Pages: 283-303 Issue: 4 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802018253 File-URL: http://hdl.handle.net/10.1080/10485250802018253 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:4:p:283-303 Template-Type: ReDIF-Article 1.0 Author-Name: Taeryon Choi Author-X-Name-First: Taeryon Author-X-Name-Last: Choi Title: Convergence of posterior distribution in the mixture of regressions Abstract: Mixture models provide a method of modelling a complex probability distribution in terms of simpler structures. In particular, the method of mixture of regressions has received considerable attention due to its modelling flexibility and availability of convenient computational algorithms. This paper aims to contribute to theoretical justification for the mixtures of regression model from the Bayesian perspective. In particular, we establish consistency of posterior distribution and determine how fast posterior distribution converges to the true value of the parameter in the context of mixture of binary, Poisson, and Gaussian regressions. Journal: Journal of Nonparametric Statistics Pages: 337-351 Issue: 4 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802018303 File-URL: http://hdl.handle.net/10.1080/10485250802018303 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:4:p:337-351 Template-Type: ReDIF-Article 1.0 Author-Name: Inkyung Jung Author-X-Name-First: Inkyung Author-X-Name-Last: Jung Author-Name: Pranab Kumar Sen Author-X-Name-First: Pranab Author-X-Name-Last: Kumar Sen Title: Robust testing for random effects in unbalanced heteroscedastic one-way models Abstract: The usual variance ratio test for random effect, in a balanced design, is quite vulnerable to (i) unbalancedness, (ii) non-normality of either of the two random components, and (iii) heteroscedasticity of the chance errors. A robust rank-based test assuming only continuous, symmetric but otherwise arbitrary distributions for both the random effect and chance errors, and for a general heteroscedastic model is proposed here. Whereas the parametric tests are based on some F-distributional approximations, the proposed rank-based test rests on a normal approximation. Simulation studies, made to support the proposed methodology, suggest that not only the test is robust with respect to its significance level but also performs better in power, for heteroscedastic unbalanced models (even under normality). Journal: Journal of Nonparametric Statistics Pages: 305-317 Issue: 4 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802018477 File-URL: http://hdl.handle.net/10.1080/10485250802018477 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:4:p:305-317 Template-Type: ReDIF-Article 1.0 Author-Name: Mingxin Wu Author-X-Name-First: Mingxin Author-X-Name-Last: Wu Author-Name: Yijun Zuo Author-X-Name-First: Yijun Author-X-Name-Last: Zuo Title: Trimmed and winsorized standard deviations based on a scaled deviation Abstract: Trimmed (and winsorized) standard deviations based on a scaled deviation are introduced and studied. The influence functions and limiting distributions are obtained. The performance of the estimators with respect to high breakdown scale estimators is evaluated and compared. Unlike other high breakdown estimators which perform poorly for light-tailed distribution and when points near the centre are contaminated, the resulting trimmed (and winsorized) standard deviations are much more efficient than their predecessors at light-tailed distributions by suitably choosing the cutting parameter and highly efficient for heavy-tailed and skewed distributions. At the same time, they share the best breakdown point robustness of the sample median absolute deviation for any common trimming thresholds. Compared with their predecessors, they can achieve the best efficiency when the contaminating points are presented from areas around the centre. Indeed, the scaled-deviation-trimmed (winsorized) standard deviations behave very well overall and, consequently, represent very favourable alternatives to existing scale estimators. Journal: Journal of Nonparametric Statistics Pages: 319-335 Issue: 4 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802036909 File-URL: http://hdl.handle.net/10.1080/10485250802036909 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:4:p:319-335 Template-Type: ReDIF-Article 1.0 Author-Name: Nengxiang Ling Author-X-Name-First: Nengxiang Author-X-Name-Last: Ling Author-Name: Shuhe Hu Author-X-Name-First: Shuhe Author-X-Name-Last: Hu Title: Asymptotic distribution of partitioning estimation and modified partitioning estimation for regression functions Abstract: Estimation of regression function from independent and identically distributed data is considered. In this paper, we investigate partitioning and modified partitioning estimation for regression functions. The asymptotic normality of partitioning and modified partitioning function estimation is shown. Journal: Journal of Nonparametric Statistics Pages: 353-363 Issue: 4 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802159198 File-URL: http://hdl.handle.net/10.1080/10485250802159198 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:4:p:353-363 Template-Type: ReDIF-Article 1.0 Author-Name: Wanrong Liu Author-X-Name-First: Wanrong Author-X-Name-Last: Liu Author-Name: Xuewen Lu Author-X-Name-First: Xuewen Author-X-Name-Last: Lu Title: Weighted least squares method for censored linear models Abstract: For estimation of linear models with randomly censored data, a class of data transformations is used to construct synthetic data. It is shown that the conditional variance of the synthetic data depends on the covariates in the model regardless of the homoscedasticity of the error. Therefore, linear models based on the synthetic data are always heteroscedastic models. To improve efficiency, we propose a weighted least squares (WLS) method, where the conditional variance of the synthetic data is estimated nonparametrically, then the standard WLS principle is applied to the synthetic data in the estimation procedure. The resultant estimator is asymptotically normal and the limiting variance is estimated using the plug-in method. In general, the proposed method improves the existing synthetic data methods for censored linear models, and gains more efficiency. For the censored heteroscedastic linear models, where the Buckley–James (BJ) and rank-based methods cannot be used since the condition of homoscedastic errors is violated, the new method provides a solution for better estimation. Monte Carlo simulations are conducted to compare the proposed method with the unweighted least squares method and the BJ method under different error conditions. Journal: Journal of Nonparametric Statistics Pages: 787-799 Issue: 7 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902795636 File-URL: http://hdl.handle.net/10.1080/10485250902795636 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:7:p:787-799 Template-Type: ReDIF-Article 1.0 Author-Name: Zhaozhi Fan Author-X-Name-First: Zhaozhi Author-X-Name-Last: Fan Author-Name: Xiao-Feng Wang Author-X-Name-First: Xiao-Feng Author-X-Name-Last: Wang Title: Marginal hazards model for multivariate failure time data with auxiliary covariates Abstract: A marginal hazards model of multivariate failure times has been developed based on the ‘working independence’ assumption [L.J. Wei, D.Y. Lin, and L. Wessfeld, Regression analysis of multivariate incomplete failure time data by modeling marginal distributions, J. Amer. Statist. Assoc. 84 (1989), pp. 1065–1073.]. In this article, we study the marginal hazards model of multivariate failure times with continuous auxiliary covariates. We consider the case of common baseline hazards for subjects from the same clusters. We extend the kernel smoothing procedure of Zhou and Wang [H. Zhou and C.Y. Wang, Failure time regression with continuous covariates measured with error, J. Roy. Statist. Soc. B 62 (2000), pp. 657–665.] to correlated failure time data. Through semiparametric estimation of the marginal partial likelihood function, we obtain the estimated partial likelihood based estimator of the regression coefficients. We present asymptotic properties of the induced estimator and demonstrate the performance of the proposed estimator through a finite sample simulation study. Finally, a real data application is conducted to elucidate the use of the method. Journal: Journal of Nonparametric Statistics Pages: 771-786 Issue: 7 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902915903 File-URL: http://hdl.handle.net/10.1080/10485250902915903 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:7:p:771-786 Template-Type: ReDIF-Article 1.0 Author-Name: Li-Ping Zhu Author-X-Name-First: Li-Ping Author-X-Name-Last: Zhu Author-Name: Li-Xing Zhu Author-X-Name-First: Li-Xing Author-X-Name-Last: Zhu Title: A data-adaptive hybrid method for dimension reduction Abstract: To gain the advantages of different inverse regression methods, the convex combination can be useful for estimating the central subspace. To select an appropriate combination coefficient in the hybrid method, we propose in this paper a data-adaptive hybrid method using the trace of kernel matrices. For ease of illustration, we consider particularly the combination of inverse regressions using the conditional mean and the conditional variance, both of which are separately powerful in estimating different models. Because the efficacy of the slicing estimation may deteriorate when it is used to estimate the conditional variance, we use the kernel smoother instead. The asymptotic normality at the root-n rate is achieved even with the data-driven combination weight. Illustrative examples by simulations and an application to horse mussel data is presented to demonstrate the necessity of the hybrid models and the efficacy of our kernel estimation. Journal: Journal of Nonparametric Statistics Pages: 851-861 Issue: 7 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902980568 File-URL: http://hdl.handle.net/10.1080/10485250902980568 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:7:p:851-861 Template-Type: ReDIF-Article 1.0 Author-Name: Peixin Zhao Author-X-Name-First: Peixin Author-X-Name-Last: Zhao Author-Name: Liugen Xue Author-X-Name-First: Liugen Author-X-Name-Last: Xue Title: Empirical likelihood inferences for semiparametric varying-coefficient partially linear errors-in-variables models with longitudinal data Abstract: In this paper, empirical likelihood inferences for semiparametric varying-coefficient partially linear error-in-variables models with longitudinal data are investigated. By correcting the attenuation, we propose a corrected empirical likelihood ratio function for the parametric components and a residual-adjusted empirical likelihood ratio function for the nonparametric components. Wilks’ phenomenon is proved and the confidence regions for parametric components and nonparametric components are constructed. A simulation study is undertaken to assess the finite sample performance of the proposed confidence regions. Journal: Journal of Nonparametric Statistics Pages: 907-923 Issue: 7 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902980576 File-URL: http://hdl.handle.net/10.1080/10485250902980576 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:7:p:907-923 Template-Type: ReDIF-Article 1.0 Author-Name: Jinfeng Xu Author-X-Name-First: Jinfeng Author-X-Name-Last: Xu Author-Name: Lincheng Zhao Author-X-Name-First: Lincheng Author-X-Name-Last: Zhao Author-Name: Chenlei Leng Author-X-Name-First: Chenlei Author-X-Name-Last: Leng Title: Statistical inference for induced L-statistics: a random perturbation approach Abstract: Suppose that X and Y are two numerical characteristics defined for each individual in a population. In a random sample of (X, Y) with sample size n, denote the rth ordered X variate by Xr:n and the associated Y variate, the induced rth order statistics, by Y[r:n], respectively. Induced order statistics arise naturally in the context of selection where individuals ought to be selected by their ranks in a related X value due to difficulty or high costs of obtaining Y at the time of selection. The induced L-statistics, which take the form of , are very useful in regression analysis, especially when the observations are subject to a type-II censoring scheme with respect to the dependent variable, or when the regression function at a given quantile of the predictor variable is of interest. The limiting variance of the induced L-statistics involve the underlying regression function and inferences based on nonparametric estimation are often unstable. In this paper, we consider the distributional approximation of the induced L-statistics by the random perturbation method. Large sample properties of the randomly perturbed induced L-statistics are established. Numerical studies are also conducted to illustrate the method and to assess its finite-sample performance. Journal: Journal of Nonparametric Statistics Pages: 863-876 Issue: 7 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902980584 File-URL: http://hdl.handle.net/10.1080/10485250902980584 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:7:p:863-876 Template-Type: ReDIF-Article 1.0 Author-Name: Samiran Sinha Author-X-Name-First: Samiran Author-X-Name-Last: Sinha Author-Name: Suojin Wang Author-X-Name-First: Suojin Author-X-Name-Last: Wang Title: A new semiparametric procedure for matched case-control studies with missing covariates Abstract: In this paper, we propose an easy-to-use semiparametric method for analysing matched case-control data when one of the covariates of interest is partially missing. Missing covariate information in matched case-control studies may create bias and reduce efficiency of the parameter estimates. In order to cope with this situation we consider a robust approach which is comprised of estimating some functionals of the distribution of the partially missing covariate using a kernel regression technique in a conditional likelihood framework. The large sample theory of the proposed estimator is investigated and the asymptotic normality is obtained. A simulation study is conducted to assess the performance of the proposed method in terms of robustness and efficiency. The proposed method is also applied to a real dataset which motivates this work. Journal: Journal of Nonparametric Statistics Pages: 889-905 Issue: 7 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250903019523 File-URL: http://hdl.handle.net/10.1080/10485250903019523 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:7:p:889-905 Template-Type: ReDIF-Article 1.0 Author-Name: Zhengyuan Zhu Author-X-Name-First: Zhengyuan Author-X-Name-Last: Zhu Author-Name: Yufeng Liu Author-X-Name-First: Yufeng Author-X-Name-Last: Liu Title: Estimating spatial covariance using penalised likelihood with weighted penalty Abstract: In spatial statistics, the estimation of covariance matrices is of great importance because of its role in spatial prediction and design. In this paper, we propose a penalised likelihood approach with weighted L1 regularisation to estimate the covariance matrix for spatial Gaussian Markov random field models with unspecified neighbourhood structures. A new algorithm for ordering spatial points is proposed such that the corresponding precision matrix can be estimated more effectively. Furthermore, we develop an efficient algorithm to minimise the penalised likelihood via a novel usage of the regularised solution path algorithm, which does not require the use of iterative algorithms. By exploiting the sparsity structure in the precision matrix, we show that the LASSO type of approach gives improved covariance estimators measured by several criteria. Asymptotic properties of our proposed estimator are derived. Both our simulated examples and an application to the rainfall data set show that the proposed method performs competitively. Journal: Journal of Nonparametric Statistics Pages: 925-942 Issue: 7 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250903023632 File-URL: http://hdl.handle.net/10.1080/10485250903023632 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:7:p:925-942 Template-Type: ReDIF-Article 1.0 Author-Name: T. Tony Cai Author-X-Name-First: T. Author-X-Name-Last: Tony Cai Author-Name: Mark Low Author-X-Name-First: Mark Author-X-Name-Last: Low Author-Name: Linda Zhao Author-X-Name-First: Linda Author-X-Name-Last: Zhao Title: Sharp adaptive estimation by a blockwise method Abstract: We consider a blockwise James–Stein estimator for nonparametric function estimation in suitable wavelet or Fourier bases. The estimator can be readily explained and implemented. We show that the estimator is asymptotically sharp adaptive in minimax risk over any Sobolev ball containing the true function. Further, for a moderately broad range of bounded sets in the Besov space our estimator is asymptotically nearly sharp adaptive in the sense that it comes within the Donoho–Liu constant, 1.24, of being exactly sharp adaptive. Other parameter spaces are also considered. The paper concludes with a Monte-Carlo study comparing the performance of our estimator with that of three other popular wavelet estimators. Our procedure generally (but not always) outperforms two of these and is overall comparable, or perhaps slightly superior, with the third. Journal: Journal of Nonparametric Statistics Pages: 839-850 Issue: 7 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250903026320 File-URL: http://hdl.handle.net/10.1080/10485250903026320 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:7:p:839-850 Template-Type: ReDIF-Article 1.0 Author-Name: Dianliang Deng Author-X-Name-First: Dianliang Author-X-Name-Last: Deng Author-Name: Hong-Bin Fang Author-X-Name-First: Hong-Bin Author-X-Name-Last: Fang Author-Name: Jianguo Sun Author-X-Name-First: Jianguo Author-X-Name-Last: Sun Title: Nonparametric estimation for doubly censored failure time data Abstract: This paper considers the nonparametric estimation of a failure time distribution function when only doubly censored data are available, which occurs in many situations such as epidemiological studies. In these situations, the failure time of interest is defined as the elapsed time between an initial event and a subsequent event, and the observations on both events can suffer censoring. As a consequence, the estimation is much more complicated than that for right- or interval-censored failure time data both theoretically and practically. For the problem, although several procedures have been proposed, they are only ad hoc approaches as the asymptotic properties of the resulting estimates are basically unknown. We investigate both the consistency and the convergence rate of a commonly used nonparametric estimate and show that as expected, the estimate is slower than that with right-censored or interval-censored data. Furthermore, we establish the asymptotic normality of the smooth functionals of the estimate and present a nonparametric test procedure for treatment comparison. Journal: Journal of Nonparametric Statistics Pages: 801-814 Issue: 7 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250903108383 File-URL: http://hdl.handle.net/10.1080/10485250903108383 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:7:p:801-814 Template-Type: ReDIF-Article 1.0 Author-Name: Q. Shao Author-X-Name-First: Q. Author-X-Name-Last: Shao Title: Seasonality analysis of time series in partial linear models Abstract: Seasonality analysis is one of the classic topics in time series. This paper studies techniques for seasonality analysis when the trend function is unspecified. The asymptotic properties of the semiparametric estimators are derived, and an estimation algorithm is provided. The techniques are applied to making inference for the monthly global land–ocean temperature anomaly indexes. Journal: Journal of Nonparametric Statistics Pages: 827-837 Issue: 7 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250903108391 File-URL: http://hdl.handle.net/10.1080/10485250903108391 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:7:p:827-837 Template-Type: ReDIF-Article 1.0 Author-Name: Caiya Zhang Author-X-Name-First: Caiya Author-X-Name-Last: Zhang Author-Name: Zhengyan Lin Author-X-Name-First: Zhengyan Author-X-Name-Last: Lin Author-Name: Jianjun Wu Author-X-Name-First: Jianjun Author-X-Name-Last: Wu Title: Nonparametric tests for the general multivariate multi-sample problem Abstract: Some nonparametric tests for the multivariate multi-sample problem are proposed in this paper. For the location–scale model, the univariate Kruskal–Wallis test and the bivariate Mardia test are generalised to the multivariate case. For the general multivariate multi-sample problem, a new test based on the Liu-Singh statistic is proposed and the asymptotic null distribution of this test statistic is established under some regularity conditions. The results of simulation show that these tests are more effective than the parametric tests when the assumption of multivariate normal distribution is violated, especially under the scale model or the location–scale model. Journal: Journal of Nonparametric Statistics Pages: 877-888 Issue: 7 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250903111684 File-URL: http://hdl.handle.net/10.1080/10485250903111684 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:7:p:877-888 Template-Type: ReDIF-Article 1.0 Author-Name: Tony Cai Author-X-Name-First: Tony Author-X-Name-Last: Cai Title: Editorial Journal: Pages: 769-769 Issue: 7 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250903142663 File-URL: http://hdl.handle.net/10.1080/10485250903142663 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:7:p:769-769 Template-Type: ReDIF-Article 1.0 Author-Name: Yiqiang Lu Author-X-Name-First: Yiqiang Author-X-Name-Last: Lu Author-Name: Riquan Zhang Author-X-Name-First: Riquan Author-X-Name-Last: Zhang Title: Smoothing spline estimation of generalised varying-coefficient mixed model Abstract: The generalised varying-coefficient model with longitudinal data faces a challenge that the data are correlated, as multiple observations are measured from each individual. In this article we consider the generalised varying-coefficient mixed model (GVCMM) which uses a varying-coefficient model to fit mean functions, while accounting for overdispersion and correlation by adding random effects. Smoothing splines are used to estimate the smooth but arbitrary nonparametric coefficient functions. The usually intractable integration involved in evaluating the quasi-likelihood function is approximated by the Laplace method. This suggests that the GVCMM can be approximately represented by a generalised linear mixed model. Hence, the smoothing parameters and the variance components can be estimated by using the restricted maximum log-likelihood (REML) approach, where the smoothing parameters are treated as an extra variance component vector. We illustrate the performance of the proposed method through some simulation and an application to a real data set. Journal: Journal of Nonparametric Statistics Pages: 815-825 Issue: 7 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250903151078 File-URL: http://hdl.handle.net/10.1080/10485250903151078 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:7:p:815-825 Template-Type: ReDIF-Article 1.0 Author-Name: Rong Liu Author-X-Name-First: Rong Author-X-Name-Last: Liu Author-Name: Lijian Yang Author-X-Name-First: Lijian Author-X-Name-Last: Yang Title: Kernel estimation of multivariate cumulative distribution function Abstract: A smooth kernel estimator is proposed for multivariate cumulative distribution functions (cdf), extending the work of Yamato [H. Yamato, Uniform convergence of an estimator of a distribution function, Bull. Math. Statist. 15 (1973), pp. 69–78.] on univariate distribution function estimation. Under assumptions of strict stationarity and geometrically strong mixing, we establish that the proposed estimator follows the same pointwise asymptotically normal distribution of the empirical cdf, while the new estimator is a smooth instead of a step function as the empirical cdf. We also show that under stronger assumptions the smooth kernel estimator has asymptotically smaller mean integrated squared error than the empirical cdf, and converges to the true cdf uniformly almost surely at a rate of (n−1/2log n). Simulated examples are provided to illustrate the theoretical properties. Using the smooth estimator, survival curves for US gross domestic product (GDP) growth are estimated conditional on the unemployment growth rate to examine how GDP growth rate depends on the unemployment policy. Another example of gold and silver price returns is given. Journal: Journal of Nonparametric Statistics Pages: 661-677 Issue: 8 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802326391 File-URL: http://hdl.handle.net/10.1080/10485250802326391 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:8:p:661-677 Template-Type: ReDIF-Article 1.0 Author-Name: Christopher Withers Author-X-Name-First: Christopher Author-X-Name-Last: Withers Author-Name: Saralees Nadarajah Author-X-Name-First: Saralees Author-X-Name-Last: Nadarajah Title: Edgeworth expansions for functions of weighted empirical distributions with applications to nonparametric confidence intervals Abstract: Given independent observations X1n, …, Xnn in Rs, let [Fcirc](x) be their weighted empirical distribution with weights w1n, …, wnn. We obtain cumulant expansions for the weighted estimate T([Fcirc]) for any smooth functional T(·) by extending the concepts of von Mises derivatives to signed measures of total measure 1. From these are derived third-order Edgeworth–Cornish–Fisher expansions for T([Fcirc]) and confidence intervals for T(F) of third-order accuracy based on the weighted empirical distribution. These results are also extended to samples from k distributions and confidence intervals for functionals of k distributions. Journal: Journal of Nonparametric Statistics Pages: 751-768 Issue: 8 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802392971 File-URL: http://hdl.handle.net/10.1080/10485250802392971 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:8:p:751-768 Template-Type: ReDIF-Article 1.0 Author-Name: Jesse Frey Author-X-Name-First: Jesse Author-X-Name-Last: Frey Title: An exact distribution-free one-sample test for equivalence Abstract: There are many exact distribution-free goodness-of-fit tests, but no equivalence testing analogues. This paper fills the gap by developing an exact one-sample distribution-free equivalence test for use with continuous distributions. We consider two continuous distributions equivalent if the pointwise distances between their distribution functions never exceed some specified constant, and we test equivalence using the supremum of the pointwise distances between the empirical distribution function and the fully specified continuous distribution of interest. The resulting test is much more powerful than a naive exact distribution-free equivalence test based on two one-sided Kolmogorov–Smirnov tests, and inversion of the test leads to distribution-free confidence bands for the unknown distribution function that are centred at the fully specified continuous distribution of interest. Journal: Journal of Nonparametric Statistics Pages: 739-750 Issue: 8 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802401053 File-URL: http://hdl.handle.net/10.1080/10485250802401053 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:8:p:739-750 Template-Type: ReDIF-Article 1.0 Author-Name: Willem Albers Author-X-Name-First: Willem Author-X-Name-Last: Albers Author-Name: Wilbert Kallenberg Author-X-Name-First: Wilbert Author-X-Name-Last: Kallenberg Title: MINDCUMIN charts Abstract: A serious drawback of classical control charts is their high sensitivity to deviations from normality. By now, many alternative procedures, often of a nonparametric nature, have been proposed. A danger with these competitors is that unrealistically large Phase I samples might be needed. This can be avoided by using groups of, rather than individual (IND), observations during Phase II. A recently introduced successful example is the CUMIN chart: a signal occurs as soon as m consecutive observations all exceed some suitably chosen upper limit. An interesting question is how m should be chosen in this cumulative minimum. If large (small) shifts are likely to occur, m should be small (large). As often the magnitude of possible shifts is unclear, it is attractive to be flexible w.r.t. the choice of m. In the present paper, a procedure is developed which achieves this goal by combining an IND and a CUMIN procedure. As input minima of small blocks (e.g. pairs or triples) of observations should be used to avoid recurrence of the problem of the need for unrealistically large Phase I samples. The nice performance of the proposed MINDCUMIN chart and its straightforward implementation make it very useful for application in practice. Journal: Journal of Nonparametric Statistics Pages: 769-790 Issue: 8 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802439533 File-URL: http://hdl.handle.net/10.1080/10485250802439533 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:8:p:769-790 Template-Type: ReDIF-Article 1.0 Author-Name: Dimitrios Bagkavos Author-X-Name-First: Dimitrios Author-X-Name-Last: Bagkavos Title: Transformations in hazard rate estimation Abstract: A new estimate of the hazard rate function is proposed, based on nonparametric transformations of the data and motivated by the bias expression of conventional kernel hazard estimates. The squared error of this estimate is considered, and it is shown to be considerably smaller than that of ordinary kernel estimates. With the use of a practical bandwidth choice rule, the estimate is illustrated graphically on distributional and real-world data. Journal: Journal of Nonparametric Statistics Pages: 721-738 Issue: 8 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802440184 File-URL: http://hdl.handle.net/10.1080/10485250802440184 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:8:p:721-738 Template-Type: ReDIF-Article 1.0 Author-Name: Melanie Birke Author-X-Name-First: Melanie Author-X-Name-Last: Birke Author-Name: Holger Dette Author-X-Name-First: Holger Author-X-Name-Last: Dette Title: A note on estimating a smooth monotone regression by combining kernel and density estimates Abstract: In a recent paper Dette, Neumeyer and Pilz (H. Dette, N. Neumeyer, and K.F. Pilz, A simple nonparametric estimator of a strictly monotone regression function, Bernoulli 12 (2006), pp. 469–490) proposed a new nonparametric estimate of a smooth monotone regression function. This method is based on a non-decreasing rearrangement of an arbitrary unconstrained nonparametric estimator. Under the assumption of a twice continuously differentiable regression function, the estimate is first-order asymptotic equivalent to the unconstrained estimate and other types of smooth monotone estimates. In this note, we provide a more refined asymptotic analysis of the monotone regression estimate. In the case where the regression function is increasing but only once continuously differentiable, we prove the asymptotic normality of an appropriately standardised version of the estimate, where the asymptotic variance is of order n−2/3−ϵ, the bias is of order n−1/3+ϵ and ϵ > 0 is small. Therefore, the rate of convergence of the new estimate is worse than the rate n−1/3 of the (unsmoothed) monotone least squares estimate. On the other hand, if the derivative of the regression function is Hölder continuous, the rate of convergence of the new estimate is faster than n−1/3. Journal: Journal of Nonparametric Statistics Pages: 679-691 Issue: 8 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802445399 File-URL: http://hdl.handle.net/10.1080/10485250802445399 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:8:p:679-691 Template-Type: ReDIF-Article 1.0 Author-Name: Elisa–María Molanes-López Author-X-Name-First: Elisa–María Author-X-Name-Last: Molanes-López Author-Name: Ricardo Cao Author-X-Name-First: Ricardo Author-X-Name-Last: Cao Title: Relative density estimation for left truncated and right censored data Abstract: In biostatistical applications, it is very common that the generation of data is subject to mechanisms of loss of information such as censoring and truncation. In this setting, the direct application of traditional methods designed for completely observed data is not suitable at all. In the setting of a two-sample problem, this paper is focused on a kernel-type relative density estimator defined for left truncated and right censored data. First of all, an asymptotic representation of the estimator is found and based on this representation, its bias, variance and limit distribution are obtained. Then, a plug-in global bandwidth selector is designed for the kernel-type relative density estimator and their performance is checked through a simulation study. Finally, the estimator and the bandwidth selector are applied to a medical data set concerning gastric adenocarcinoma. Journal: Journal of Nonparametric Statistics Pages: 693-720 Issue: 8 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802447882 File-URL: http://hdl.handle.net/10.1080/10485250802447882 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:8:p:693-720 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: List of reviewers Journal: Pages: 791-792 Issue: 8 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802542401 File-URL: http://hdl.handle.net/10.1080/10485250802542401 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:8:p:791-792 Template-Type: ReDIF-Article 1.0 Author-Name: Xianyan Chen Author-X-Name-First: Xianyan Author-X-Name-Last: Chen Author-Name: Qingcong Yuan Author-X-Name-First: Qingcong Author-X-Name-Last: Yuan Author-Name: Xiangrong Yin Author-X-Name-First: Xiangrong Author-X-Name-Last: Yin Title: Sufficient dimension reduction via distance covariance with multivariate responses Abstract: In this article, we propose a new method for sufficient dimension reduction when both response and predictor are vectors. The new method, using distance covariance, keeps the model-free advantage, and can fully recover the central subspace even when many predictors are discrete. We then extend this method to the dual central subspace, including a special case of canonical correlation analysis. We illustrated estimators through extensive simulations and real datasets, and compared to some existing methods, showing that our estimators are competitive and robust. Journal: Journal of Nonparametric Statistics Pages: 268-288 Issue: 2 Volume: 31 Year: 2019 Month: 4 X-DOI: 10.1080/10485252.2018.1562065 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1562065 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:2:p:268-288 Template-Type: ReDIF-Article 1.0 Author-Name: Luo Xiao Author-X-Name-First: Luo Author-X-Name-Last: Xiao Title: Asymptotics of bivariate penalised splines Abstract: We study the class of bivariate penalised splines that use tensor product splines and a smoothness penalty. Similar to Claeskens, G., Krivobokova, T., and Opsomer, J.D. [(2009), ‘Asymptotic Properties of Penalised Spline Estimators’, Biometrika, 96(3), 529–544] for the univariate penalised splines, we show that, depending on the number of knots and penalty, the global asymptotic convergence rate of bivariate penalised splines is either similar to that of tensor product regression splines or to that of thin plate splines. In each scenario, the bivariate penalised splines are found rate optimal in the sense of Stone, C.J. [(12, 1982), ‘Optimal Global Rates of Convergence for Nonparametric Regression’, The Annals of Statistics, 10(4), 1040–1053] for a corresponding class of functions with appropriate smoothness. For the scenario where a small number of knots is used, we obtain expressions for the local asymptotic bias and variance and derive the point-wise and uniform asymptotic normality. The theoretical results are applicable to tensor product regression splines. Journal: Journal of Nonparametric Statistics Pages: 289-314 Issue: 2 Volume: 31 Year: 2019 Month: 4 X-DOI: 10.1080/10485252.2018.1563295 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1563295 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:2:p:289-314 Template-Type: ReDIF-Article 1.0 Author-Name: Qiqing Yu Author-X-Name-First: Qiqing Author-X-Name-Last: Yu Author-Name: Qinggang Diao Author-X-Name-First: Qinggang Author-X-Name-Last: Diao Title: Consistency of The MMGLE under the piecewise proportional hazards models with interval-censored data Abstract: Wong et al. [(2018), ‘Piece-wise Proportional Hazards Models with Interval-censored Data’, Journal of Statistical Computation and Simulation, 88, 140–155] studied the piecewise proportional hazards (PWPH) model with interval-censored (IC) data under the distribution-free set-up. It is well known that the partial likelihood approach is not applicable for IC data, and Wong et al. (2018) showed that the standard generalised likelihood approach does not work either. They proposed the maximum modified generalised likelihood estimator (MMGLE) and the simulation results suggest that the MMGLE is consistent. We establish the consistency and asymptotically normality of the MMGLE. Journal: Journal of Nonparametric Statistics Pages: 315-321 Issue: 2 Volume: 31 Year: 2019 Month: 4 X-DOI: 10.1080/10485252.2018.1563296 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1563296 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:2:p:315-321 Template-Type: ReDIF-Article 1.0 Author-Name: S. Anjana Author-X-Name-First: S. Author-X-Name-Last: Anjana Author-Name: Isha Dewan Author-X-Name-First: Isha Author-X-Name-Last: Dewan Author-Name: K. K. Sudheesh Author-X-Name-First: K. K. Author-X-Name-Last: Sudheesh Title: Test for independence between time to failure and cause of failure in competing risks with k causes Abstract: In this paper, we develop a simple nonparametric test for testing the independence of time to failure and cause of failure in competing risks set up. We generalise the test to the situation where failure data is right censored. We obtain the asymptotic distribution of the test statistics for complete and censored data. The efficiency loss due to censoring is studied using Pitman efficiency. The performance of the proposed test is evaluated through simulations. Finally we illustrate our test procedure using three real data sets. Journal: Journal of Nonparametric Statistics Pages: 322-339 Issue: 2 Volume: 31 Year: 2019 Month: 4 X-DOI: 10.1080/10485252.2018.1563699 File-URL: http://hdl.handle.net/10.1080/10485252.2018.1563699 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:2:p:322-339 Template-Type: ReDIF-Article 1.0 Author-Name: Mengmei Xi Author-X-Name-First: Mengmei Author-X-Name-Last: Xi Author-Name: Xuejun Wang Author-X-Name-First: Xuejun Author-X-Name-Last: Wang Title: On the rates of asymptotic normality for recursive kernel density estimators under ϕ-mixing assumptions Abstract: In this paper, we mainly consider two kinds of recursive kernel estimators of $ f(x) $ f(x), which is the probability density function of a sequence of ϕ-mixing random variables $ \{X_i, i\geq 1\} $ {Xi,i≥1}. Under some suitable conditions, we establish the convergence rates of asymptotic normality for the two recursive kernel estimators $ \hat {f}_n(x)=({1}/{n\sqrt {b_n}})\sum _{j=1}^nb_j^{-{1}/{2}}K({(x-X_j)}/{b_j}) $ fˆn(x)=(1/nbn)∑j=1nbj−1/2K((x−Xj)/bj) and $ \tilde {f}_n(x)=({1}/{n})\sum _{j=1}^n({1}/{b_j})K ({(x-X_j)}/{b_j}) $ f~n(x)=(1/n)∑j=1n(1/bj)K((x−Xj)/bj). In particular, by the choice of the bandwidths, the convergence rates of asymptotic normality for the estimators $ \hat {f}_n(x) $ fˆn(x) and $ \tilde {f}_n(x) $ f~n(x) can attain $ O(n^{-{1}/{8}}\log ^{{1}/{3}}n) $ O(n−1/8log1/3⁡n) and $ O(n^{-{1}/{6}}\log ^{{1}/{3}}n), $ O(n−1/6log1/3⁡n), respectively. Besides, the simulation study and a real data analysis are presented to verify the validity of the theoretical results. Journal: Journal of Nonparametric Statistics Pages: 340-363 Issue: 2 Volume: 31 Year: 2019 Month: 4 X-DOI: 10.1080/10485252.2019.1566542 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1566542 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:2:p:340-363 Template-Type: ReDIF-Article 1.0 Author-Name: Silvia Novo Author-X-Name-First: Silvia Author-X-Name-Last: Novo Author-Name: Germán Aneiros Author-X-Name-First: Germán Author-X-Name-Last: Aneiros Author-Name: Philippe Vieu Author-X-Name-First: Philippe Author-X-Name-Last: Vieu Title: Automatic and location-adaptive estimation in functional single-index regression Abstract: This paper develops a new automatic and location-adaptive procedure for estimating regression in a Functional Single-Index Model (FSIM). This procedure is based on k-Nearest Neighbours (kNN) ideas. The asymptotic study includes results for automatically data-driven selected number of neighbours, making the procedure directly usable in practice. The local feature of the kNN approach insures higher predictive power compared with usual kernel estimates, as illustrated in some finite sample analysis. As by-product, we state as preliminary tools some new uniform asymptotic results for kernel estimates in the FSIM model. Journal: Journal of Nonparametric Statistics Pages: 364-392 Issue: 2 Volume: 31 Year: 2019 Month: 4 X-DOI: 10.1080/10485252.2019.1567726 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1567726 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:2:p:364-392 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Kohler Author-X-Name-First: Michael Author-X-Name-Last: Kohler Author-Name: Adam Krzyżak Author-X-Name-First: Adam Author-X-Name-Last: Krzyżak Title: Estimation of extreme quantiles in a simulation model Abstract: A simulation model with an outcome $ Y=m(X) $ Y=m(X) is considered, where X is an $ {\mathbb {R}^d} $ Rd-valued random variable and $ m: {\mathbb {R}^d} \rightarrow \mathbb{R} $ m:Rd→R is a smooth function. Estimates of the $ \alpha _n $ αn-quantile $ q_{m(X),\alpha _n} $ qm(X),αn of $ m(X) $ m(X) based on surrogate model of m and on importance sampling are constructed which use at most n evaluations of the function m. Results concerning the rate of convergence of the estimates are derived in case that $ \alpha _n \rightarrow 1 $ αn→1 $ (n \rightarrow \infty ) $ (n→∞) and $ n \cdot (1-\alpha _n) \rightarrow 0 $ n⋅(1−αn)→0 $ (n \rightarrow \infty ) $ (n→∞). Finite sample behaviour of the estimates is illustrated by simulations. Journal: Journal of Nonparametric Statistics Pages: 393-419 Issue: 2 Volume: 31 Year: 2019 Month: 4 X-DOI: 10.1080/10485252.2019.1567727 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1567727 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:2:p:393-419 Template-Type: ReDIF-Article 1.0 Author-Name: Ji Chen Author-X-Name-First: Ji Author-X-Name-Last: Chen Author-Name: Fang Fang Author-X-Name-First: Fang Author-X-Name-Last: Fang Title: Semiparametric likelihood for estimating equations with non-ignorable non-response by non-response instrument Abstract: Non-response or missing data is a common phenomenon in many areas. Non-ignorable non-response, a response mechanism that depends on the values of the variable having non-response, is the most difficult type of non-response to handle. This paper considers statistical inference of unknown parameters in estimating equations (EEs) when the variable of interest has non-ignorable non-response. By utilising the cutting edge techniques of non-response instrument, a parametric response propensity function can be identified and estimated. Then a semiparametric likelihood is constructed with the propensity function, EEs and auxiliary information being incorporated into the constraints to make the inference valid and improve the estimation efficiency. Asymptotic distributions for the resulting parameter estimates are derived. Empirical results including two simulation studies and a real example show that the proposed method gives promising results. Journal: Journal of Nonparametric Statistics Pages: 420-434 Issue: 2 Volume: 31 Year: 2019 Month: 4 X-DOI: 10.1080/10485252.2019.1569664 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1569664 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:2:p:420-434 Template-Type: ReDIF-Article 1.0 Author-Name: Zhenghui Feng Author-X-Name-First: Zhenghui Author-X-Name-Last: Feng Author-Name: Yujie Gai Author-X-Name-First: Yujie Author-X-Name-Last: Gai Author-Name: Jun Zhang Author-X-Name-First: Jun Author-X-Name-Last: Zhang Title: Correlation curve estimation for multiplicative distortion measurement errors data Abstract: A correlation curve measures the strength of the association between two variables locally at different values of covariate. This paper studies how to estimate the correlation curve under the multiplicative distortion measurement errors setting. The unobservable variables are both distorted in a multiplicative fashion by an observed confounding variable. We obtain asymptotic normality results for the estimated correlation curve. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimator. The estimated correlation curve is applied to analyze a real dataset for an illustration. Journal: Journal of Nonparametric Statistics Pages: 435-450 Issue: 2 Volume: 31 Year: 2019 Month: 4 X-DOI: 10.1080/10485252.2019.1580708 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1580708 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:2:p:435-450 Template-Type: ReDIF-Article 1.0 Author-Name: Nengxiang Ling Author-X-Name-First: Nengxiang Author-X-Name-Last: Ling Author-Name: Shuyu Meng Author-X-Name-First: Shuyu Author-X-Name-Last: Meng Author-Name: Philippe Vieu Author-X-Name-First: Philippe Author-X-Name-Last: Vieu Title: Uniform consistency rate of kNN regression estimation for functional time series data Abstract: In this paper, we investigate the k-nearest neighbours (kNN) estimation of nonparametric regression model for strong mixing functional time series data. More precisely, we establish the uniform almost complete convergence rate of the kNN estimator under some mild conditions. Furthermore, a simulation study and an empirical application to the real data analysis of sea surface temperature (SST) are carried out to illustrate the finite sample performances and the usefulness of the kNN approach. Journal: Journal of Nonparametric Statistics Pages: 451-468 Issue: 2 Volume: 31 Year: 2019 Month: 4 X-DOI: 10.1080/10485252.2019.1583338 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1583338 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:2:p:451-468 Template-Type: ReDIF-Article 1.0 Author-Name: Shangyuan Ye Author-X-Name-First: Shangyuan Author-X-Name-Last: Ye Author-Name: Ye Liang Author-X-Name-First: Ye Author-X-Name-Last: Liang Author-Name: Ibrahim A. Ahmad Author-X-Name-First: Ibrahim A. Author-X-Name-Last: Ahmad Title: Orthogonal series density estimation for complex surveys Abstract: We propose an orthogonal series density estimator for complex surveys, where samples are neither independent nor identically distributed. The proposed estimator is proved to be design-unbiased and asymptotically design-consistent. The asymptotic normality is proved under both design and combined spaces. Two data driven estimators are proposed based on the proposed oracle estimator. We show the efficiency of the proposed estimators in simulation studies. A real survey data example is provided for an illustration. Journal: Journal of Nonparametric Statistics Pages: 469-481 Issue: 2 Volume: 31 Year: 2019 Month: 4 X-DOI: 10.1080/10485252.2019.1585539 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1585539 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:2:p:469-481 Template-Type: ReDIF-Article 1.0 Author-Name: Radhakanta Das Author-X-Name-First: Radhakanta Author-X-Name-Last: Das Title: A distribution-free approach for selecting better treatment through an ethical allocation Abstract: The present article provides a statistical inference on comparative performances of two treatments in a clinical trial under a two-stage adaptive allocation design. Suppose a fixed number (2m+n, say) of subjects are available for treatment by any of the two competing treatments, say, A and B for a particular ailment. As per the proposed allocation design, $ 2m $ 2m incoming subjects are randomised equally between A and B at the first stage. Then, at the second stage, the remaining n subjects are exclusively assigned to the treatment which has higher observed median response evaluated in the first stage. Under such an ethical allocation design we decide on the better treatment through an asymptotically distribution-free test procedure. The related asymptotic results are also studied. Journal: Journal of Nonparametric Statistics Pages: 482-505 Issue: 2 Volume: 31 Year: 2019 Month: 4 X-DOI: 10.1080/10485252.2019.1597083 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1597083 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:2:p:482-505 Template-Type: ReDIF-Article 1.0 Author-Name: Manon Costa Author-X-Name-First: Manon Author-X-Name-Last: Costa Author-Name: Sébastien Gadat Author-X-Name-First: Sébastien Author-X-Name-Last: Gadat Author-Name: Pauline Gonnord Author-X-Name-First: Pauline Author-X-Name-Last: Gonnord Author-Name: Laurent Risser Author-X-Name-First: Laurent Author-X-Name-Last: Risser Title: Cytometry inference through adaptive atomic deconvolution Abstract: In this paper, we consider a statistical estimation problem known as atomic deconvolution. Introduced in reliability, this model has a direct application when considering biological data produced by flow cytometers. From a statistical point of view, we aim at inferring the percentage of cells expressing the selected molecule and the probability distribution function associated with its fluorescence emission. We propose here an adaptive estimation procedure based on a previous deconvolution procedure introduced by Es, Gugushvili, and Spreij [(2008), ‘Deconvolution for an atomic distribution’, Electronic Journal of Statistics, 2, 265–297] and Gugushvili, Es, and Spreij [(2011), ‘Deconvolution for an atomic distribution: rates of convergence’, Journal of Nonparametric Statistics, 23, 1003–1029]. For both estimating the mixing parameter and the mixing density automatically, we use the Lepskii method based on the optimal choice of a bandwidth using a bias-variance decomposition. We then derive some convergence rates that are shown to be minimax optimal (up to some log terms) in Sobolev classes. Finally, we apply our algorithm on the simulated and real biological data. Journal: Journal of Nonparametric Statistics Pages: 506-547 Issue: 2 Volume: 31 Year: 2019 Month: 4 X-DOI: 10.1080/10485252.2019.1599376 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1599376 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:2:p:506-547 Template-Type: ReDIF-Article 1.0 Author-Name: Gérard Biau Author-X-Name-First: Gérard Author-X-Name-Last: Biau Author-Name: Kevin Bleakley Author-X-Name-First: Kevin Author-X-Name-Last: Bleakley Author-Name: László Györfi Author-X-Name-First: László Author-X-Name-Last: Györfi Author-Name: György Ottucsák Author-X-Name-First: György Author-X-Name-Last: Ottucsák Title: Nonparametric sequential prediction of time series Abstract: Time series prediction covers a vast field of everyday statistical applications in medical, environmental and economic domains. In this paper, we develop nonparametric prediction strategies based on the combination of a set of ‘experts’ and show the universal consistency of these strategies under a minimum of conditions. We perform an in-depth analysis of real-world data sets and show that these nonparametric strategies are more flexible, faster and generally outperform ARMA methods in terms of normalised cumulative prediction error. Journal: Journal of Nonparametric Statistics Pages: 297-317 Issue: 3 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250802680730 File-URL: http://hdl.handle.net/10.1080/10485250802680730 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:3:p:297-317 Template-Type: ReDIF-Article 1.0 Author-Name: Ansgar Steland Author-X-Name-First: Ansgar Author-X-Name-Last: Steland Title: A surveillance procedure for random walks based on local linear estimation Abstract: We study the problem of detecting a change in the trend of time series whose stochastic part behaves as a random walk. Interesting applications in finance and engineering come to mind. Local linear estimation provides a well established approach to estimating level and derivative of an underlying trend function, provided the time instants where observations are available become dense asymptotically. Here we study the local linear estimation principle for the classic time series setting where the distance between time points is fixed. It turns out that local linear estimation is applicable to the detection problem, and we identify the underlying (asymptotic) parameters. Assuming that observations arrive sequentially, we propose surveillance procedures and establish the relevant asymptotic theory, particularly, an invariance principle for the sequential empirical local linear process. A simulation study illustrates the remarkable accuracy of the approximations obtained by our asymptotics even in small samples as well as the excellent detection performance of the proposed surveillance procedure. Journal: Journal of Nonparametric Statistics Pages: 345-361 Issue: 3 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903082414 File-URL: http://hdl.handle.net/10.1080/10485250903082414 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:3:p:345-361 Template-Type: ReDIF-Article 1.0 Author-Name: Raquel Menezes Author-X-Name-First: Raquel Author-X-Name-Last: Menezes Author-Name: Pilar García-Soidán Author-X-Name-First: Pilar Author-X-Name-Last: García-Soidán Author-Name: Célia Ferreira Author-X-Name-First: Célia Author-X-Name-Last: Ferreira Title: Nonparametric spatial prediction under stochastic sampling design Abstract: In this work, the nonparametric kernel prediction will be considered for spatial stochastic processes when a stochastic sampling design is assumed for selection of locations. We will prove that under rather general conditions, the mean-squared prediction error tends to be negligible as the sample size increases. However, use of the optimal bandwidth demands the estimation of unknown quantities, whose accurate approximation can often be difficult in practice. Hence, alternative cross-validation approaches will be provided for the selection of both local and global bandwidths. Numerical studies were carried out in order to analyse the performance of the nonparametric predictor for both simulated and real data. Journal: Journal of Nonparametric Statistics Pages: 363-377 Issue: 3 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903094294 File-URL: http://hdl.handle.net/10.1080/10485250903094294 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:3:p:363-377 Template-Type: ReDIF-Article 1.0 Author-Name: Irène Gijbels Author-X-Name-First: Irène Author-X-Name-Last: Gijbels Author-Name: Anneleen Verhasselt Author-X-Name-First: Anneleen Author-X-Name-Last: Verhasselt Title: Regularisation and P-splines in generalised linear models Abstract: P-splines regression is a flexible smoothing tool in which the starting point is a highly parameterised model and overfitting is prevented by introducing a penalty function. A common form of the penalty term is obtained by taking a prespecified order of differences of adjacent coefficients. This paper deals with a data-driven choice of the differencing order, as such allowing for the fit to adapt automatically to the (unknown) degree of smoothness of the underlying function. The selection procedure is based on Akaike's information criterion. The study is carried out in a broad framework of generalised linear and generalised additive models. We provide the necessary theoretical support for the selection procedure, and investigate its performance via simulations. We illustrate the use of such a selection procedure on some real data examples. The discussed examples include generalised normal, binomial and Poisson regression models. Journal: Journal of Nonparametric Statistics Pages: 271-295 Issue: 3 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903365900 File-URL: http://hdl.handle.net/10.1080/10485250903365900 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:3:p:271-295 Template-Type: ReDIF-Article 1.0 Author-Name: Jacobo de Uña-Álvarez Author-X-Name-First: Jacobo Author-X-Name-Last: de Uña-Álvarez Author-Name: Han-Ying Liang Author-X-Name-First: Han-Ying Author-X-Name-Last: Liang Author-Name: Alberto Rodríguez-Casal Author-X-Name-First: Alberto Author-X-Name-Last: Rodríguez-Casal Title: Nonlinear wavelet estimator of the regression function under left-truncated dependent data Abstract: In this paper, we define a new nonlinear wavelet-based estimator of the regression function under random left-truncation. We provide an asymptotic expression for the mean integrated squared error (MISE) of the estimator. It is assumed that the observations form a stationary α-mixing sequence. The nonlinear wavelet-based estimator of the covariate's density is considered as well. Unlike for kernel estimators, the MISE expression of the wavelet-based estimators is not affected by the presence of discontinuities in the curves. The finite sample behaviour of the proposed estimators is explored through simulations. Journal: Journal of Nonparametric Statistics Pages: 319-344 Issue: 3 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903469736 File-URL: http://hdl.handle.net/10.1080/10485250903469736 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:3:p:319-344 Template-Type: ReDIF-Article 1.0 Author-Name: P. Sankaran Author-X-Name-First: P. Author-X-Name-Last: Sankaran Author-Name: N. Unnikrishnan Nair Author-X-Name-First: N. Author-X-Name-Last: Unnikrishnan Nair Title: Nonparametric estimation of hazard quantile function Abstract: In this paper, we study the estimation of the hazard quantile function based on right censored data. Two nonparametric estimators, one based on the empirical quantile density function and the other using the kernel smoothing method, are proposed. Asymptotic properties of the kernel-based estimator are discussed. Monte Carlo simulation studies are conducted to compare the two estimators. The method is illustrated for a real data set. Journal: Journal of Nonparametric Statistics Pages: 757-767 Issue: 6 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902919046 File-URL: http://hdl.handle.net/10.1080/10485250902919046 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:6:p:757-767 Template-Type: ReDIF-Article 1.0 Author-Name: Cong Li Author-X-Name-First: Cong Author-X-Name-Last: Li Author-Name: Desheng Ouyang Author-X-Name-First: Desheng Author-X-Name-Last: Ouyang Author-Name: Jeffrey Racine Author-X-Name-First: Jeffrey Author-X-Name-Last: Racine Title: Nonparametric regression with weakly dependent data: the discrete and continuous regressor case Abstract: Data-driven methods of bandwidth selection are necessary for the sound application of kernel methods, with benefits including but not limited to automatic dimensionality reduction in the presence of irrelevant regressors [P. Hall, Q. Li, and J.S. Racine, ‘Nonparametric estimation of regression functions in the presence of irrelevant regressors, Rev. Econ. Statist. 89 (2007), pp. 784–789] and the ability to handle the mix of discrete and continuous data often encountered in applied settings without resorting to sample splitting [J.S. Racine and Q. Li, Nonparametric estimation of regression functions with both categorical and continuous data, J. Econometrics 119(1) (2004), pp. 99–130]. Many existing results have been developed under the presumption of independence, which may not hold when one deals with time-series data. This paper develops the properties of data-driven kernel regression for weakly dependent mixed discrete and continuous data. Monte Carlo simulations are undertaken to examine the finite-sample properties of the estimator, and an illustrative application is presented. Journal: Journal of Nonparametric Statistics Pages: 697-711 Issue: 6 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902928435 File-URL: http://hdl.handle.net/10.1080/10485250902928435 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:6:p:697-711 Template-Type: ReDIF-Article 1.0 Author-Name: Laurent Cavalier Author-X-Name-First: Laurent Author-X-Name-Last: Cavalier Author-Name: Nicolas Hengartner Author-X-Name-First: Nicolas Author-X-Name-Last: Hengartner Title: Estimating linear functionals in Poisson mixture models Abstract: This paper concerns the problem of estimating linear functionals of the mixing distribution from Poisson mixture observations. In particular, linear functionals for which a parametric rate of convergence cannot be achieved are studied. It appears that Gaussian functionals are rather easy to estimate. Estimation of the distribution functions is then considered by approximating this functional using Gaussian functionals. Finally, the case of smooth distribution functions is considered in order to deal with rather general linear functionals. Journal: Journal of Nonparametric Statistics Pages: 713-728 Issue: 6 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902971716 File-URL: http://hdl.handle.net/10.1080/10485250902971716 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:6:p:713-728 Template-Type: ReDIF-Article 1.0 Author-Name: B. Pateiro-López Author-X-Name-First: B. Author-X-Name-Last: Pateiro-López Author-Name: A. Rodríguez-Casal Author-X-Name-First: A. Author-X-Name-Last: Rodríguez-Casal Title: Surface area estimation under convexity type assumptions Abstract: The problem of estimating the surface area, L0, of a set G⊂ℝd has been extensively considered in several fields of research. For example, stereology focuses on the estimation of L0 without needing to reconstruct the set G. From a more geometrical point of view, set estimation theory is interested in estimating the shape of the set. Thus, surface area estimation can be seen as a further step where the emphasis is placed on an important geometric characteristic of G. The Minkowski content is an attractive way to define L0 that has been previously used in the literature on surface area estimation. Pateiro-López and Rodríguez-Casal [B. Pateiro-López and A. Rodríguez-Casal, Length and surface area estimation under smoothness restrictions, Adv. Appl. Prob. 40(2) (2008), pp. 348–358] proposed an estimator, Ln, for L0 under convexity type assumptions. In this paper, we obtain the L1-convergence rate of Ln. Journal: Journal of Nonparametric Statistics Pages: 729-741 Issue: 6 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902971732 File-URL: http://hdl.handle.net/10.1080/10485250902971732 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:6:p:729-741 Template-Type: ReDIF-Article 1.0 Author-Name: Haiyan Wang Author-X-Name-First: Haiyan Author-X-Name-Last: Wang Author-Name: Michael Akritas Author-X-Name-First: Michael Author-X-Name-Last: Akritas Title: Rank tests in heteroscedastic multi-way HANOVA Abstract: This article develops rank tests for the nonparametric main factor effects and interactions in multi-way high-dimensional analysis of variance when the cell distributions are completely unspecified. The design can be balanced or unbalanced with the cell sample sizes fixed or tending to infinity. An arbitrary number of factors and all types of ordinal data are allowed. This extends the use of rank methods to the Neymann–Scott and triangular array problems. The asymptotic distribution of the rank statistics is obtained by showing their asymptotic equivalence to corresponding expressions based on the asymptotic rank transform. Compared with test procedures based on the original observations, the proposed rank procedures are free of moment conditions, converge to their limiting distribution faster, and have better power when the underlying distributions are heavy tailed or skewed. These advantages are demonstrated by simulations and an application to a real data set. Journal: Journal of Nonparametric Statistics Pages: 663-681 Issue: 6 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902971757 File-URL: http://hdl.handle.net/10.1080/10485250902971757 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:6:p:663-681 Template-Type: ReDIF-Article 1.0 Author-Name: Zhengyan Lin Author-X-Name-First: Zhengyan Author-X-Name-Last: Lin Author-Name: Yanbiao Xiang Author-X-Name-First: Yanbiao Author-X-Name-Last: Xiang Author-Name: Caiya Zhang Author-X-Name-First: Caiya Author-X-Name-Last: Zhang Title: Adaptive Lasso in high-dimensional settings Abstract: Huang et al. [J. Huang, S. Ma, and C.-H. Zhang, Adaptive Lasso for sparse high-dimensional regression models, Statist. Sinica 18 (2008), pp. 1603–1618] have studied the asymptotic properties of the adaptive Lasso estimators in sparse, high-dimensional, linear regression models when the number of covariates may increase with the sample size. They proved that the adaptive Lasso has an oracle property in the sense of Fan and Li [J. Fan and R. Li, Variable selection via nonconcave penalized likelihood and its oracle properties, J. Am. Statist. Assoc. 96 (2001), pp. 1348–1360] and Fan and Peng [J. Fan and H. Peng, Nonconcave penalized likelihood with a diverging number of parameters, Ann. Statist. 32 (2004), pp. 928–961] under appropriate conditions. Particularly, they assumed that the errors of the linear regression model have Gaussian tails. In this paper, we relax this condition and assume that the errors have the finite 2kth moment for an integer k>0. With this assumption, we prove that the adaptive Lasso also has the oracle property under some appropriate conditions. Simulations are carried out to provide understanding of our result. Journal: Journal of Nonparametric Statistics Pages: 683-696 Issue: 6 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902984875 File-URL: http://hdl.handle.net/10.1080/10485250902984875 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:6:p:683-696 Template-Type: ReDIF-Article 1.0 Author-Name: B. Brown Author-X-Name-First: B. Author-X-Name-Last: Brown Author-Name: Robert Newcombe Author-X-Name-First: Robert Author-X-Name-Last: Newcombe Author-Name: Yudong Zhao Author-X-Name-First: Yudong Author-X-Name-Last: Zhao Title: Non-null semi-parametric inference for the Mann–Whitney measure Abstract: A simple method is introduced for finding large sample, boundary-respecting confidence intervals (CIs) for the two-sample Mann–Whitney measure, θ=Pr{X>Y}−Pr{X<Y}. This natural separation measure for two distributions occurs in stress–strength models, receiver operating characteristic curves, and nonparametrics generally. The usual estimate of θ is a centred version of the well-known Mann–Whitney statistic. Previous Wald-type CIs are not boundary-respecting. The difficulty is typically nonparametric, whereby appealing exact distributions hold only for one null parameter value, preventing the formulation of true distribution-free inference for non-null values. Here, the rank method setting and a result, that stochastic ordering is equivalent to monotone transformation of location shift, allow the assumption that data derive from a smooth location shift family. A suitable class of location shift families then model the asymptotic variance, leading to a rapidly converging iterative CI method based on roots of quadratics. Simulations show that the proposed method performs at least as well, or better, than competing CI methods. Journal: Journal of Nonparametric Statistics Pages: 743-755 Issue: 6 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902999162 File-URL: http://hdl.handle.net/10.1080/10485250902999162 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:6:p:743-755 Template-Type: ReDIF-Article 1.0 Author-Name: Lan Wang Author-X-Name-First: Lan Author-X-Name-Last: Wang Author-Name: Michael Akritas Author-X-Name-First: Michael Author-X-Name-Last: Akritas Author-Name: Ingrid Van Keilegom Author-X-Name-First: Ingrid Author-X-Name-Last: Van Keilegom Title: An ANOVA-type nonparametric diagnostic test for heteroscedastic regression models Abstract: For the heteroscedastic nonparametric regression model Yni=m (xni)+σ (xni) εni, i=1, …, n, we discuss a novel method for testing some parametric assumptions about the regression function m. The test is motivated by recent developments in the asymptotic theory for analysis of variance when the number of factor levels is large. Asymptotic normality of the test statistic is established under the null hypothesis and suitable local alternatives. The similarity of the form of the test statistic to that of the classical F-statistic in analysis of variance allows easy and fast calculation. Simulation studies demonstrate that the new test possesses satisfactory finite-sample properties. Journal: Journal of Nonparametric Statistics Pages: 365-382 Issue: 5 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802066112 File-URL: http://hdl.handle.net/10.1080/10485250802066112 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:5:p:365-382 Template-Type: ReDIF-Article 1.0 Author-Name: John Reber Author-X-Name-First: John Author-X-Name-Last: Reber Author-Name: Jeff Terpstra Author-X-Name-First: Jeff Author-X-Name-Last: Terpstra Author-Name: Xianzhe Chen Author-X-Name-First: Xianzhe Author-X-Name-Last: Chen Title: Weighted -estimates for a VAR() time series model Abstract: The most common method of estimating the parameters of a vector-valued autoregressive time series model is the method of least squares (LS). However, since LS estimates are sensitive to the presence of outliers, more robust techniques are often useful. This paper investigates one such technique, weighted-L1 estimates. Following traditional methods of proof, asymptotic uniform linearity and asymptotic uniform quadricity results are established. Additionally, the gradient of the objective function is shown to be asymptotically normal. These results imply that the weighted-L1 parameter estimates for this model are asymptotically normal at rate n−1/2. The results rely heavily on covariance inequalities for geometric absolutely regular processes and a Martingale central limit theorem. Estimates for the asymptotic variance–covariance matrix are also discussed. A finite-sample efficiency study is presented to examine the performance of the weighted-L1 estimate in the presence of both innovation and additive outliers. Specifically, the classical LS estimate is compared with three versions of the weighted- L1 estimate. Finally, a quadravariate financial time series is used to demonstrate the estimation procedure. A brief residual analysis is also presented. Journal: Journal of Nonparametric Statistics Pages: 395-411 Issue: 5 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802151898 File-URL: http://hdl.handle.net/10.1080/10485250802151898 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:5:p:395-411 Template-Type: ReDIF-Article 1.0 Author-Name: Alejandro Quintela-Del-Río Author-X-Name-First: Alejandro Author-X-Name-Last: Quintela-Del-Río Title: Hazard function given a functional variable: Non-parametric estimation under strong mixing conditions Abstract: We study here the kernel type, non-parametric estimation of the conditional hazard function, based on a sample of functional dependent data. The almost complete convergence of the conditional hazard estimate is easily derived using the properties referred by Ferraty et al for the conditional distribution and conditional density estimates. The asymptotic bias and variances of the three estimates (conditional density, distribution and hazard) are calculated and compared with the results obtained in p-dimensional non-parametric kernel estimation. The asymptotic normality is established for the three mentioned estimates. Finally, an application to an earthquake data set is made. Journal: Journal of Nonparametric Statistics Pages: 413-430 Issue: 5 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802159297 File-URL: http://hdl.handle.net/10.1080/10485250802159297 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:5:p:413-430 Template-Type: ReDIF-Article 1.0 Author-Name: Zhiyi Zhang Author-X-Name-First: Zhiyi Author-X-Name-Last: Zhang Author-Name: Hongwei Huang Author-X-Name-First: Hongwei Author-X-Name-Last: Huang Title: A sufficient normality condition for Turing's formula Abstract: This paper establishes a previously unknown sufficient condition for the asymptotic normality of the non-parametric sample coverage estimate based on Good under a fixed underlying probability distribution {pk; k=1, …} where all pk>0. The sufficient condition of this paper supports a non-empty class of distributions and excludes the condition of Esty as a marginal case in which it is shown that the √n-normalised sample coverage estimate proposed by Esty necessarily degenerates under a fixed {pk}. The convergent statistic in the newly established normality law and the resulting relevant confidence intervals are all of new forms, and specifically are different from those suggested by Esty. Journal: Journal of Nonparametric Statistics Pages: 431-446 Issue: 5 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802172126 File-URL: http://hdl.handle.net/10.1080/10485250802172126 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:5:p:431-446 Template-Type: ReDIF-Article 1.0 Author-Name: Rosa Giancristofaro Author-X-Name-First: Rosa Author-X-Name-Last: Giancristofaro Author-Name: Stefano Bonnini Author-X-Name-First: Stefano Author-X-Name-Last: Bonnini Title: Moment-based multivariate permutation tests for ordinal categorical data Abstract: Stochastic dominance problems in testing for ordered categorical variables are of specific interest in performance analysis, because they are frequently encountered in practice and present distinctive difficulties, especially within the framework of likelihood ratio tests. Until now, the literature has essentially considered the univariate case, and several solutions have been proposed to cope with it, most of which are based on restricted maximum likelihood ratio tests. These solutions are generally criticised, because the degree of accuracy of their asymptotic null and alternative distributions is difficult to assess and characterise. In this paper, we propose a new exact solution based on a simultaneous analysis of a finite set of sampling moments of ranks, or general scores, assigned to ordered classes and processed within a permutation approach. Journal: Journal of Nonparametric Statistics Pages: 383-393 Issue: 5 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802195440 File-URL: http://hdl.handle.net/10.1080/10485250802195440 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:5:p:383-393 Template-Type: ReDIF-Article 1.0 Author-Name: Antonio Lijoi Author-X-Name-First: Antonio Author-X-Name-Last: Lijoi Author-Name: Igor Prünster Author-X-Name-First: Igor Author-X-Name-Last: Prünster Author-Name: S. Walker Author-X-Name-First: S. Author-X-Name-Last: Walker Title: Posterior analysis for some classes of nonparametric models Abstract: Recently, James [L.F. James, Bayesian Poisson process partition calculus with an application to Bayesian Lévy moving averages, Ann. Statist. 33 (2005), pp. 1771–1799.] and [L.F. James, Poisson calculus for spatial neutral to the right processes, Ann. Statist. 34 (2006), pp. 416–440.] has derived important results for various models in Bayesian nonparametric inference. In particular, in ref. [L.F. James, Poisson calculus for spatial neutral to the right processes, Ann. Statist. 34 (2006), pp. 416–440.] a spatial version of neutral to the right processes is defined and their posterior distribution derived. Moreover, in ref. [L.F. James, Bayesian Poisson process partition calculus with an application to Bayesian Lévy moving averages, Ann. Statist. 33 (2005), pp. 1771–1799.] the posterior distribution for an intensity or hazard rate modelled as a mixture under a general multiplicative intensity model is obtained. His proofs rely on the so-called Bayesian Poisson partition calculus. Here we provide alternative proofs based on a different technique. Journal: Journal of Nonparametric Statistics Pages: 447-457 Issue: 5 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802196364 File-URL: http://hdl.handle.net/10.1080/10485250802196364 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:5:p:447-457 Template-Type: ReDIF-Article 1.0 Author-Name: Zhihua Sun Author-X-Name-First: Zhihua Author-X-Name-Last: Sun Author-Name: Yifan Jiang Author-X-Name-First: Yifan Author-X-Name-Last: Jiang Author-Name: Xue Ye Author-X-Name-First: Xue Author-X-Name-Last: Ye Title: Improved statistical inference on semiparametric varying-coefficient partially linear measurement error model Abstract: In this paper, we consider the estimation and goodness-of-fit test of a semiparametric varying-coefficient partially linear (SVCPL) model when both responses and part of covariates are measured with error. It is assumed that the true variables are measurable functions of some auxiliary variables. The often-used assumptions on the measurement error, such as a known error variance, a known distribution of the error variable, a validation sample or a repeated data set, are not required. The asymptotic properties of the proposed estimators and testing statistic are investigated. We show that the application of the measurement error structures can improve the efficiency of estimating and testing methods. The performances of the estimating and testing methods are illustrated by simulation studies and an application to a real data set. Journal: Journal of Nonparametric Statistics Pages: 549-566 Issue: 3 Volume: 31 Year: 2019 Month: 7 X-DOI: 10.1080/10485252.2019.1603383 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1603383 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:3:p:549-566 Template-Type: ReDIF-Article 1.0 Author-Name: Rida Benhaddou Author-X-Name-First: Rida Author-X-Name-Last: Benhaddou Author-Name: Qing Liu Author-X-Name-First: Qing Author-X-Name-Last: Liu Title: Anisotropic functional deconvolution with long-memory noise: the case of a multi-parameter fractional Wiener sheet Abstract: We look into the minimax results for the anisotropic two-dimensional functional deconvolution model with the two-parameter fractional Gaussian noise. We derive the lower bounds for the $L^p $Lp-risk, $1 \leq p < \infty $1≤p<∞, and taking advantage of the Riesz poly-potential, we apply a wavelet-vaguelette expansion to de-correlate the anisotropic fractional Gaussian noise. We construct an adaptive wavelet hard-thresholding estimator that attains asymptotically optimal or quasi-optimal convergence rates in a wide range of Besov balls. Such convergence rates depend on a delicate balance between the parameters of the Besov balls, the degree of ill-posedness of the convolution operator and the parameters of the fractional Gaussian noise under regular-smooth convolution, whereas the rates are not affected by long-memory under super-smooth convolution. A limited simulations study confirms the theoretical claims of the paper. The proposed approach is extended to the general r-dimensional case, with r>2, and the corresponding convergence rates do not suffer from the curse of dimensionality. Journal: Journal of Nonparametric Statistics Pages: 567-595 Issue: 3 Volume: 31 Year: 2019 Month: 7 X-DOI: 10.1080/10485252.2019.1604953 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1604953 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:3:p:567-595 Template-Type: ReDIF-Article 1.0 Author-Name: Jian Shi Author-X-Name-First: Jian Author-X-Name-Last: Shi Author-Name: Anna Liu Author-X-Name-First: Anna Author-X-Name-Last: Liu Author-Name: Yuedong Wang Author-X-Name-First: Yuedong Author-X-Name-Last: Wang Title: Spline density estimation and inference with model-based penalties Abstract: In this paper we propose model-based penalties for smoothing spline density estimation and inference. These model-based penalties incorporate indefinite prior knowledge that the density is close to, but not necessarily in a family of distributions. We will use the Pearson and generalisation of the generalised inverse Gaussian families to illustrate the derivation of penalties and reproducing kernels. We also propose new inference procedures to test the hypothesis that the density belongs to a specific family of distributions. We conduct extensive simulations to show that the model-based penalties can substantially reduce both bias and variance in the decomposition of the Kullback-Leibler distance, and the new inference procedures are more powerful than some existing ones. We further demonstrate the empirical performance of the proposed method with a real world data set. Journal: Journal of Nonparametric Statistics Pages: 596-611 Issue: 3 Volume: 31 Year: 2019 Month: 7 X-DOI: 10.1080/10485252.2019.1606219 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1606219 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:3:p:596-611 Template-Type: ReDIF-Article 1.0 Author-Name: E. A. Pchelintsev Author-X-Name-First: E. A. Author-X-Name-Last: Pchelintsev Author-Name: V. A. Pchelintsev Author-X-Name-First: V. A. Author-X-Name-Last: Pchelintsev Author-Name: S. M. Pergamenshchikov Author-X-Name-First: S. M. Author-X-Name-Last: Pergamenshchikov Title: Improved robust model selection methods for a Lévy nonparametric regression in continuous time Abstract: In this paper, we develop the James–Stein improved method for the estimation problem of a nonparametric periodic function observed with Lévy noises in continuous time. An adaptive model selection procedure based on the weighted improved least squares estimates is constructed. The improvement effect for nonparametric models is studied. It turns out that in non-asymptotic setting the accuracy improvement for nonparametric models is more important than for parametric ones. Moreover, sharp oracle inequalities for the robust risks have been shown and the adaptive efficiency property for the proposed procedures has been established. The numerical simulations are given. Journal: Journal of Nonparametric Statistics Pages: 612-628 Issue: 3 Volume: 31 Year: 2019 Month: 7 X-DOI: 10.1080/10485252.2019.1609672 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1609672 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:3:p:612-628 Template-Type: ReDIF-Article 1.0 Author-Name: Włodzimierz Wysocki Author-X-Name-First: Włodzimierz Author-X-Name-Last: Wysocki Title: Integral generators of Archimedean n-copulas Abstract: We introduce two algebraic structures induced by an Archimedean n-copula: a one-parameter group of transformations and a one-parameter local group of transformations. We then study the natural functional characteristics (integral generators) of these structures. We discuss differential equations joining the integral generators and the additive generators of copulas. We show that the algebraic structures can be recovered by using a certain parametric family of differential equations. Finally, we give some applications of integral generators, and we indicate potential applications of the algebraic and analytical results obtained. Journal: Journal of Nonparametric Statistics Pages: 629-662 Issue: 3 Volume: 31 Year: 2019 Month: 7 X-DOI: 10.1080/10485252.2019.1626382 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1626382 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:3:p:629-662 Template-Type: ReDIF-Article 1.0 Author-Name: Da Xu Author-X-Name-First: Da Author-X-Name-Last: Xu Author-Name: Shishun Zhao Author-X-Name-First: Shishun Author-X-Name-Last: Zhao Author-Name: Tao Hu Author-X-Name-First: Tao Author-X-Name-Last: Hu Author-Name: Jianguo Sun Author-X-Name-First: Jianguo Author-X-Name-Last: Sun Title: Regression analysis of informatively interval-censored failure time data with semiparametric linear transformation model Abstract: Regression analysis of interval-censored failure time data with noninformative censoring has been widely investigated and many methods have been proposed. Sometimes the mechanism behind the interval censoring may be informative and several approaches have also been developed for this latter situation. However, all of these existing methods are for single models and it is well known that in many situations, one may prefer more flexible models. Corresponding to this, the linear transformation model is considered and a maximum likelihood estimation method is established. In the proposed method, the association between the failure time of interest and the censoring time is modelled by the copula model, and the involved nonparametric functions are approximated by spline functions. The large sample properties of the proposed estimators are derived. Numerical results show that the proposed method performs well in practical application. Besides, a real data example is presented for the illustration. Journal: Journal of Nonparametric Statistics Pages: 663-679 Issue: 3 Volume: 31 Year: 2019 Month: 7 X-DOI: 10.1080/10485252.2019.1626383 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1626383 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:3:p:663-679 Template-Type: ReDIF-Article 1.0 Author-Name: Xiaomeng Niu Author-X-Name-First: Xiaomeng Author-X-Name-Last: Niu Author-Name: Hyunkeun Ryan Cho Author-X-Name-First: Hyunkeun Ryan Author-X-Name-Last: Cho Title: Adjusting for baseline information in comparing the efficacy of treatments using bivariate varying-coefficient models Abstract: In biomedical studies, patients' reaction to the treatment can be different depending on their health condition at baseline. In this paper, we develop a bivariate varying-coefficient regression model for longitudinal data with the baseline outcome. The proposed model enables the exploration of the dynamic trend of response variables over time and to provide an effective treatment based on an individual's baseline level of disease by allowing the coefficients to vary with time and baseline. The varying coefficients are modelled through basis function approximation and a set of basis functions is selected by the proposed criterion based on the empirical loglikelihood. After the proposed model is fitted to data, the hypothesis test is designed to evaluate the efficacy of treatments across baseline levels. Theoretical and empirical studies confirm that the proposed methods choose the most parsimonious model consistently and compare the treatment effects successfully across baseline levels. The entire procedure is illustrated with depression data analysis. Journal: Journal of Nonparametric Statistics Pages: 680-694 Issue: 3 Volume: 31 Year: 2019 Month: 7 X-DOI: 10.1080/10485252.2019.1626384 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1626384 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:3:p:680-694 Template-Type: ReDIF-Article 1.0 Author-Name: Jinglan Li Author-X-Name-First: Jinglan Author-X-Name-Last: Li Author-Name: Zhengjun Zhang Author-X-Name-First: Zhengjun Author-X-Name-Last: Zhang Title: Hierarchical time-varying mixed-effects models in high-dimensional time series and longitudinal data studies Abstract: We propose time-varying coefficient mixed-effects models for continuous multiple time series data and longitudinal data. The challenge is how to simultaneously display serial, clustering, and multivariate attributes of the data set, to which the routinely assumed two-level hierarchical model and univariate response models are not able to apply. Asymptotic properties of the proposed methods are established. We also conduct the model comparison, and find that the proposed methods outperform the traditional univariate response models, nonparametric models, and linear mixed effects models in both predicting the response and estimating the coefficient surface based on simulation studies. Finally, we have applied our methods to a real-world study on the price–volume relationship of NASDAQ stock market data. Journal: Journal of Nonparametric Statistics Pages: 695-721 Issue: 3 Volume: 31 Year: 2019 Month: 7 X-DOI: 10.1080/10485252.2019.1629436 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1629436 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:3:p:695-721 Template-Type: ReDIF-Article 1.0 Author-Name: Qiang Wu Author-X-Name-First: Qiang Author-X-Name-Last: Wu Author-Name: Paul Vos Author-X-Name-First: Paul Author-X-Name-Last: Vos Title: Permutation inference distribution for linear regression and related models Abstract: For linear regression and related models, a permutation inference distribution (PID) is introduced. Like the confidence distribution in the Bayesian/Fiducial/Frequentist inference framework, the PID allows the construction of both confidence intervals and p-values. For two-sample problems and pairwise comparisons in ANOVA models, a fast Fourier transformation method can be used to find the exact PID. In general, however, random permutations are required except for small samples where all $n! $n! permutations can be generated. Simulation studies and real data applications are used to evaluate inferences obtained from the PID. PID methods are close to standard parametric methods when the errors are iid and normal. For skewed and heavy tailed errors, PID methods are superior to bootstrap and standard parametric methods. Journal: Journal of Nonparametric Statistics Pages: 722-742 Issue: 3 Volume: 31 Year: 2019 Month: 7 X-DOI: 10.1080/10485252.2019.1632306 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1632306 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:3:p:722-742 Template-Type: ReDIF-Article 1.0 Author-Name: Dongdong Xiang Author-X-Name-First: Dongdong Author-X-Name-Last: Xiang Author-Name: Shulin Gao Author-X-Name-First: Shulin Author-X-Name-Last: Gao Author-Name: Wendong Li Author-X-Name-First: Wendong Author-X-Name-Last: Li Author-Name: Xiaolong Pu Author-X-Name-First: Xiaolong Author-X-Name-Last: Pu Author-Name: Wen Dou Author-X-Name-First: Wen Author-X-Name-Last: Dou Title: A new nonparametric monitoring of data streams for changes in location and scale via Cucconi statistic Abstract: Many distribution-free control charts have been proposed for jointly monitoring location and scale parameters of a continuous distribution when their in-control (IC) status are unknown in advance. Unfortunately, most existing methods require relatively large amount of historical observations to estimate the IC parameters or to activate the control chart, and batch observations to construct the charting statistic. When such assumptions are invalid, they may not be reliable for online monitoring. In this paper, we propose a novel distribution-free control chart for joint monitoring of location and scale parameters with extremely small IC sample size. The proposed control chart integrates the Cucconi test into the framework of change-point detection and exponentially weighted moving average strategy. It requires no prior knowledge of the underlying distribution, and is very robust in start-up situations. Comprehensive numerical results show that the proposed chart is superior to its competitors. Journal: Journal of Nonparametric Statistics Pages: 743-760 Issue: 3 Volume: 31 Year: 2019 Month: 7 X-DOI: 10.1080/10485252.2019.1632307 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1632307 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:3:p:743-760 Template-Type: ReDIF-Article 1.0 Author-Name: Guangren Yang Author-X-Name-First: Guangren Author-X-Name-Last: Yang Author-Name: Hongmei Lin Author-X-Name-First: Hongmei Author-X-Name-Last: Lin Author-Name: Heng Lian Author-X-Name-First: Heng Author-X-Name-Last: Lian Title: On double-index dimension reduction for partially functional data Abstract: In this note, we consider the situation where we have a functional predictor as well as some more traditional scalar predictors, which we call the partially functional problem. We propose a semiparametric model based on sufficient dimension reduction, and thus our main interest is in dimension reduction although prediction can be carried out at a second stage. We establish root-n consistency of the linear part of the estimator. Some Monte Carlo studies are carried out as proof of concept. Journal: Journal of Nonparametric Statistics Pages: 761-768 Issue: 3 Volume: 31 Year: 2019 Month: 7 X-DOI: 10.1080/10485252.2019.1632308 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1632308 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:3:p:761-768 Template-Type: ReDIF-Article 1.0 Author-Name: Yucheng Sun Author-X-Name-First: Yucheng Author-X-Name-Last: Sun Title: Detecting price jumps in the presence of market microstructure noise Abstract: In this paper we design a test to detect the arrivals of jumps in asset prices contaminated by market microstructure noise. This test is defined by means of the truncated two-scales realised volatility estimator, recently introduced in Brownlees, Nualart, and Sun [2019, ‘On the Estimation of Integrated Volatility in the Presence of Jumps and Microstructure Noise’, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2791342.], which is a robust estimator of the realised volatility in the presence of price jumps and market microstructure noise. We derive the asymptotic value of the power of the test given the significance level, and provide conditions for the test to be consistent. Simulations show that the test performs satisfactorily when the sampling frequency is high. In particular, we show that the test performs better than some prevalent jump tests. We also provide a real data example to illustrate the proposed method. Journal: Journal of Nonparametric Statistics Pages: 769-793 Issue: 3 Volume: 31 Year: 2019 Month: 7 X-DOI: 10.1080/10485252.2019.1643019 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1643019 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:3:p:769-793 Template-Type: ReDIF-Article 1.0 Author-Name: Priyanka Majumder Author-X-Name-First: Priyanka Author-X-Name-Last: Majumder Author-Name: Murari Mitra Author-X-Name-First: Murari Author-X-Name-Last: Mitra Title: A test of exponentiality against ℳ alternatives Abstract: This paper introduces a test for detecting moment generating function order dominance. We develop a family of scale-invariant test statistics based on the weighted integrals of the difference between the empirical moment generating function and the mgf of an appropriate exponential distribution. The asymptotic distributions of our test statistics are derived and consistency of the test is established. We compute the local approximate Bahadur efficiency of the test against certain typical alternatives. The performance of the test is assessed by means of a simulation study. A suitable modification of the test under random censorship is also studied. Finally, we apply the test to some well-known real-life data sets for illustration in both the scenarios. Journal: Journal of Nonparametric Statistics Pages: 794-812 Issue: 3 Volume: 31 Year: 2019 Month: 7 X-DOI: 10.1080/10485252.2019.1643464 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1643464 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:31:y:2019:i:3:p:794-812 Template-Type: ReDIF-Article 1.0 Author-Name: Rongrong Xu Author-X-Name-First: Rongrong Author-X-Name-Last: Xu Author-Name: Jinde Wang Author-X-Name-First: Jinde Author-X-Name-Last: Wang Title: -estimation for spatial nonparametric regression Abstract: Assuming the structure of a mixing spatial data process {(Yi, Xi), i∈ℝN}, the least absolute deviation (L1) method is proposed to estimate the spatial conditional regression function with the superiority of weakening the influence of outliers and aberrant observations, which appear very often in spatial data. With appropriate choices of the bandwidth under some mild conditions imposed on the spatial process, the asymptotic distributions of the estimators are derived. Three simulation models using L1 and L2 methods respectively show that the L1-estimators are superior to L2-estimators. Journal: Journal of Nonparametric Statistics Pages: 523-537 Issue: 6 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250801976717 File-URL: http://hdl.handle.net/10.1080/10485250801976717 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:6:p:523-537 Template-Type: ReDIF-Article 1.0 Author-Name: Christian Wagner Author-X-Name-First: Christian Author-X-Name-Last: Wagner Author-Name: Ulrich Stadtmüller Author-X-Name-First: Ulrich Author-X-Name-Last: Stadtmüller Title: Asymptotics for TAYLEX and SIMEX estimators in deconvolution of densities Abstract: We deal with deconvolution problems in density estimation. Assume that the data follow a density, which is a convolution of the original density f being of interest with a noise density fϵ. In order to estimate the density f, one usually should know fϵ completely and then uses some technique for deconvolution. In contrast, the so-called TAYLEX and SIMEX methods introduced by Carroll and Hall and Cook and Stefanski, respectively use partial information on fϵ only and correct the naive density estimator towards the deconvoluted one. In the present paper, we assume that we have more and more information on the noise density when the sample size increases. We show that by applying these methods, one can achieve almost optimal rates and optimal rates respectively for densities f belonging to certain Sobolev classes. Journal: Journal of Nonparametric Statistics Pages: 507-522 Issue: 6 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802051064 File-URL: http://hdl.handle.net/10.1080/10485250802051064 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:6:p:507-522 Template-Type: ReDIF-Article 1.0 Author-Name: Danh Nguyen Author-X-Name-First: Danh Author-X-Name-Last: Nguyen Author-Name: Damla şentürk Author-X-Name-First: Damla Author-X-Name-Last: şentürk Author-Name: Raymond Carroll Author-X-Name-First: Raymond Author-X-Name-Last: Carroll Title: Covariate-adjusted linear mixed effects model with an application to longitudinal data Abstract: Linear mixed effects (LME) models are useful for longitudinal data/repeated measurements. We propose a new class of covariate-adjusted LME models for longitudinal data that nonparametrically adjusts for a normalising covariate. The proposed approach involves fitting a parametric LME model to the data after adjusting for the nonparametric effects of a baseline confounding covariate. In particular, the effect of the observable covariate on the response and predictors of the LME model is modelled nonparametrically via smooth unknown functions. In addition to covariate-adjusted estimation of fixed/population parameters and random effects, an estimation procedure for the variance components is also developed. Numerical properties of the proposed estimators are investigated with simulation studies. The consistency and convergence rates of the proposed estimators are also established. An application to a longitudinal data set on calcium absorption, accounting for baseline distortion from body mass index, illustrates the proposed methodology. Journal: Journal of Nonparametric Statistics Pages: 459-481 Issue: 6 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802226435 File-URL: http://hdl.handle.net/10.1080/10485250802226435 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:6:p:459-481 Template-Type: ReDIF-Article 1.0 Author-Name: Maria Jácome Author-X-Name-First: Maria Author-X-Name-Last: Jácome Author-Name: Ricardo Cao Author-X-Name-First: Ricardo Author-X-Name-Last: Cao Title: Asymptotic-based bandwidth selection for the presmoothed density estimator with censored data Abstract: This paper is concerned with the problem of selecting a suitable bandwidth for the presmoothed density estimator from right-censored data. An asymptotic expression for the mean integrated squared error (MISE) of this estimator is given, and the smoothing parameters minimising it are proved to be consistent approximations of the MISE bandwidths. As a consequence, a bandwidth selector based on plug-in ideas is introduced. We also present a bootstrap bandwidth selector. The performance of both methods is investigated in a simulation study, in which the Kaplan–Meier kernel density estimator has been taken as a relevant competitor. Journal: Journal of Nonparametric Statistics Pages: 483-506 Issue: 6 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802280226 File-URL: http://hdl.handle.net/10.1080/10485250802280226 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:6:p:483-506 Template-Type: ReDIF-Article 1.0 Author-Name: Helena Jansen Van Rensburg Author-X-Name-First: Helena Author-X-Name-Last: Jansen Van Rensburg Author-Name: Jan Swanepoel Author-X-Name-First: Jan Author-X-Name-Last: Swanepoel Title: A class of goodness-of-fit tests based on a new characterization of the exponential distribution Abstract: A new characterisation of the exponential distribution in the class of new better than used in expectation (NBUE) life distributions is presented. Utilising this characterisation, a new class of goodness-of-fit tests for exponentiality against NBUE alternatives is proposed. The tests are shown to be consistent, and the limiting distributions of the test statistics under the null and alternative hypotheses are derived. The newly proposed tests are compared to existing goodness-of-fit tests by means of Pitman and approximate Bahadur relative efficiencies. A limited Monte Carlo study is conducted to compare the various tests with regard to power for small and moderate sample sizes against a range of alternative distributions. Three members of the class of test statistics are identified as being at least as effective as established tests for exponentiality against NBUE alternatives. Journal: Journal of Nonparametric Statistics Pages: 539-551 Issue: 6 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802280242 File-URL: http://hdl.handle.net/10.1080/10485250802280242 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:6:p:539-551 Template-Type: ReDIF-Article 1.0 Author-Name: Jialiang Li Author-X-Name-First: Jialiang Author-X-Name-Last: Li Author-Name: Bee Tai Author-X-Name-First: Bee Author-X-Name-Last: Tai Author-Name: David Nott Author-X-Name-First: David Author-X-Name-Last: Nott Title: Confidence interval for the bootstrap -value and sample size calculation of the bootstrap test Abstract: The use of the bootstrap test lends both elegance and simplicity to the analysis of complicated statistical problems. Such a numerical approach yields an estimated P-value as a binomial proportion. The purpose of this article is to recommend that confidence intervals for the bootstrap P-value be calculated routinely. In constructing these intervals, due consideration needs to be given to the P-values that may be close to or equal to zero. We consider three instructive examples and related methods for designing the bootstrap sample size. Journal: Journal of Nonparametric Statistics Pages: 649-661 Issue: 5 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902770035 File-URL: http://hdl.handle.net/10.1080/10485250902770035 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:5:p:649-661 Template-Type: ReDIF-Article 1.0 Author-Name: Hongxia Wang Author-X-Name-First: Hongxia Author-X-Name-Last: Wang Author-Name: Jinde Wang Author-X-Name-First: Jinde Author-X-Name-Last: Wang Title: Estimation of the trend function for spatio-temporal models Abstract: Spatiotemporal models have been applied in several scientific disciplines. A crucial problem is estimation of the trend function. Although nonparametric regression for spatial data has been studied in many papers, it is not the case for spatio-temporal data. In this article, we propose a local linear fitting method for spatio-temporal data and investigate the problem under what conditions the proposed method can work well. To guarantee the uniformly weakly consistent and asymptotically normal properties, it is just required that at a fixed location i0, {R(i0, t), t∈Tn} is strictly stationary, at a fixed moment t0, {R(i, t0), i∈Λn} is strictly stationary which is weaker than {R(i, t), i∈Λn, t∈Tn} is strictly stationary both in time and space locations. This assumption can be met often in practice, and the proposed estimation method can be applied widely. The simulation results and case study show that the estimator performs well. Journal: Journal of Nonparametric Statistics Pages: 567-588 Issue: 5 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902783608 File-URL: http://hdl.handle.net/10.1080/10485250902783608 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:5:p:567-588 Template-Type: ReDIF-Article 1.0 Author-Name: Qiongxia Song Author-X-Name-First: Qiongxia Author-X-Name-Last: Song Author-Name: Lijian Yang Author-X-Name-First: Lijian Author-X-Name-Last: Yang Title: Spline confidence bands for variance functions Abstract: Asymptotically exact and conservative confidence bands are obtained for possibly heteroscedastic variance functions, using piecewise constant and piecewise linear spline estimation, respectively. The variance estimation is as efficient as an infeasible estimator when the conditional mean function is known, and the widths of the confidence bands are of optimal order. Simulation experiments provide strong evidence that corroborates the asymptotic theory while the computing is extremely fast. A slower bootstrap band is also proposed, with much higher accuracy. As illustrations, the bootstrap spline band has been applied to test for heteroscedasticity in fossil data and in motorcycle data. Journal: Journal of Nonparametric Statistics Pages: 589-609 Issue: 5 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902811151 File-URL: http://hdl.handle.net/10.1080/10485250902811151 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:5:p:589-609 Template-Type: ReDIF-Article 1.0 Author-Name: Nicholas Kiefer Author-X-Name-First: Nicholas Author-X-Name-Last: Kiefer Author-Name: Jeffrey Racine Author-X-Name-First: Jeffrey Author-X-Name-Last: Racine Title: The smooth Colonel meets the Reverend Abstract: Kernel smoothing techniques have attracted much attention and some notoriety in recent years. The attention is well deserved as kernel methods free researchers from having to impose rigid parametric structure on their data. The notoriety arises from the fact that the amount of smoothing (i.e., local averaging) that is appropriate for the problem at hand is under the control of the researcher. In this study we provide a deeper understanding of kernel smoothing methods for discrete data by leveraging the unexplored links between hierarchical Bayes models and kernel methods for discrete processes. Several potentially useful results are thereby obtained, including bounds on when kernel smoothing can be expected to dominate non-smooth (e.g., parametric) approaches in mean squared error and suggestions for thinking about the appropriate amount of smoothing. Journal: Journal of Nonparametric Statistics Pages: 521-533 Issue: 5 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902818792 File-URL: http://hdl.handle.net/10.1080/10485250902818792 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:5:p:521-533 Template-Type: ReDIF-Article 1.0 Author-Name: Guillermo Henry Author-X-Name-First: Guillermo Author-X-Name-Last: Henry Author-Name: Daniela Rodriguez Author-X-Name-First: Daniela Author-X-Name-Last: Rodriguez Title: Robust nonparametric regression on Riemannian manifolds Abstract: In this study, we introduce two families of robust kernel-based regression estimators when the regressors are random objects taking values in a Riemannian manifold. The first proposal is a local M-estimator based on kernel methods, adapted to the geometry of the manifold. For the second proposal, the weights are based on k-nearest neighbour kernel methods. Strong uniform consistent results as well as the asymptotical normality of both families are established. Finally, a Monte Carlo study is carried out to compare the performance of the robust proposed estimators with that of the classical ones, in normal and contaminated samples and a cross-validation method is discussed. Journal: Journal of Nonparametric Statistics Pages: 611-628 Issue: 5 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902846439 File-URL: http://hdl.handle.net/10.1080/10485250902846439 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:5:p:611-628 Template-Type: ReDIF-Article 1.0 Author-Name: Laura Aspirot Author-X-Name-First: Laura Author-X-Name-Last: Aspirot Author-Name: Karine Bertin Author-X-Name-First: Karine Author-X-Name-Last: Bertin Author-Name: Gonzalo Perera Author-X-Name-First: Gonzalo Author-X-Name-Last: Perera Title: Asymptotic normality of the Nadaraya–Watson estimator for nonstationary functional data and applications to telecommunications Abstract: We study a nonparametric regression model, where the explanatory variable is nonstationary dependent functional data and the response variable is scalar. Assuming that the explanatory variable is a nonstationary mixture of stationary processes and general conditions of dependence of the observations (implied in particular by weak dependence), we obtain the asymptotic normality of the Nadaraya–Watson estimator. Under some additional regularity assumptions on the regression function, we obtain asymptotic confidence intervals for the regression function. We apply this result to estimate the quality of service for an end-to-end connection on a network. Journal: Journal of Nonparametric Statistics Pages: 535-551 Issue: 5 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902878655 File-URL: http://hdl.handle.net/10.1080/10485250902878655 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:5:p:535-551 Template-Type: ReDIF-Article 1.0 Author-Name: Degui Li Author-X-Name-First: Degui Author-X-Name-Last: Li Author-Name: Jia Chen Author-X-Name-First: Jia Author-X-Name-Last: Chen Author-Name: Zhengyan Lin Author-X-Name-First: Zhengyan Author-X-Name-Last: Lin Title: Variable selection in partially time-varying coefficient models Abstract: A partially time-varying coefficient model is introduced to characterise the nonlinearity and trending phenomenon. To enhance predictability and to select significant variables in the parametric component of the model, the penalised least squares method with the help of the profile local linear technique is developed in this article. The convergence rate and the oracle property of the resulting estimator are established under mild conditions. A remarkable achievement of our results is that it does not require undersmoothing of the nonparametric component. Meanwhile, some extensions of the proposed model and method are also discussed. Furthermore, some numerical examples are provided to show that our theory and method work well in practice. Journal: Journal of Nonparametric Statistics Pages: 553-566 Issue: 5 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902912694 File-URL: http://hdl.handle.net/10.1080/10485250902912694 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:5:p:553-566 Template-Type: ReDIF-Article 1.0 Author-Name: Marco Marozzi Author-X-Name-First: Marco Author-X-Name-Last: Marozzi Title: Some notes on the location–scale Cucconi test Abstract: The best known and most used rank test for the location–scale problem is due to Lepage [Y. Lepage, A combination of Wilcoxon's and Ansari–Bradley's statistics, Biometrika 58 (1971), pp. 213–217.], but this paper is focused on the location–scale rank test of Cucconi [O. Cucconi, Un nuovo test non parametrico per il confronto tra due gruppi campionari, Giorn. Econom. XXVII (1968), pp. 225–248.], proposed earlier but not nearly as well-known. The test is of interest because, contrary to the other location–scale tests, it is not a quadratic form combining a test for location and a test for scale differences, and it is based on squared ranks and squared contrary-ranks. Moreover, it is easier to compute the test of Cucconi than those of Lepage, Manly–Francis, Büning–Thadewald, Neuhäuser, Büning and Murakami. Exact critical values for the test have been computed for the very first time. The power of the Cucconi test has been studied for the very first time and compared with that of the Lepage and other tests that include several Podgor–Gastwirth efficiency robust tests. Simulations show that the test of Cucconi maintains a size very close to α and is more powerful than the Lepage test, and therefore should be taken into account as a better alternative when it is not possible to develop an efficiency robust procedure for the problem at hand. The simulation study considers also the case of different shapes for the parent distributions, and the case of tied observations which is generally not considered in power studies. The presence of ties does not lower the performance of the Cucconi test, the contrary happens for the Lepage test. The tests are applied to real and fictitious biomedical data. Journal: Journal of Nonparametric Statistics Pages: 629-647 Issue: 5 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902952435 File-URL: http://hdl.handle.net/10.1080/10485250902952435 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:5:p:629-647 Template-Type: ReDIF-Article 1.0 Author-Name: Joshua Habiger Author-X-Name-First: Joshua Author-X-Name-Last: Habiger Author-Name: Edsel Peña Author-X-Name-First: Edsel Author-X-Name-Last: Peña Title: Randomised -values and nonparametric procedures in multiple testing Abstract: The validity of many multiple hypothesis testing procedures for false discovery rate (FDR) control relies on the assumption that P-value statistics are uniformly distributed under the null hypotheses. However, this assumption fails if the test statistics have discrete distributions or if the distributional model for the observables is misspecified. A stochastic process framework is introduced that, with the aid of a uniform variate, admits P-value statistics to satisfy the uniformity condition even when test statistics have discrete distributions. This allows nonparametric tests to be used to generate P-value statistics satisfying the uniformity condition. The resulting multiple testing procedures are therefore endowed with robustness properties. Simulation studies suggest that nonparametric randomised test P-values allow for these FDR methods to perform better when the model for the observables is nonparametric or misspecified. Journal: Journal of Nonparametric Statistics Pages: 583-604 Issue: 3 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.482154 File-URL: http://hdl.handle.net/10.1080/10485252.2010.482154 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:583-604 Template-Type: ReDIF-Article 1.0 Author-Name: Jan Johannes Author-X-Name-First: Jan Author-X-Name-Last: Johannes Author-Name: Suhasini Rao Author-X-Name-First: Suhasini Author-X-Name-Last: Rao Title: Nonparametric estimation for dependent data Abstract: In this paper, we consider nonparametric estimation for dependent data, where the observations do not necessarily come from a linear process. We study density estimation and also discuss associated problems in nonparametric regression, using the 2-mixing dependence measure. We compare the results under the 2-mixing with those derived under the assumption that the process is linear. Journal: Journal of Nonparametric Statistics Pages: 661-681 Issue: 3 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.484491 File-URL: http://hdl.handle.net/10.1080/10485252.2010.484491 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:661-681 Template-Type: ReDIF-Article 1.0 Author-Name: Zhenyu Liu Author-X-Name-First: Zhenyu Author-X-Name-Last: Liu Author-Name: Reza Modarres Author-X-Name-First: Reza Author-X-Name-Last: Modarres Title: A triangle test for equality of distribution functions in high dimensions Abstract: A triangle statistic is proposed for testing the equality of two multivariate continuous distributions in high-dimensional settings based on sample interpoint distances. Given two independent p-dimensional random samples, a triangle can be formed by randomly selecting one observation from one sample and two observations from the other sample. The triangle statistic estimates the probability that the distance between the two observations from the same distribution is the largest, the middle or the smallest in the triangle being formed by these three observations. We show that the test based on the triangle statistic is asymptotically distribution-free under the null hypothesis of equal, but unknown continuous distribution functions. The triangle test is compared with other nonparametric tests through a simulation study. The triangle statistic is well defined when the number of variables p is larger than the number of observations m, and its computational complexity is independent of p, making it suitable for high-dimensional settings. Journal: Journal of Nonparametric Statistics Pages: 605-615 Issue: 3 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.485644 File-URL: http://hdl.handle.net/10.1080/10485252.2010.485644 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:605-615 Template-Type: ReDIF-Article 1.0 Author-Name: Jialiang Li Author-X-Name-First: Jialiang Author-X-Name-Last: Li Author-Name: Wenyang Zhang Author-X-Name-First: Wenyang Author-X-Name-Last: Zhang Author-Name: Zhengxiao Wu Author-X-Name-First: Zhengxiao Author-X-Name-Last: Wu Title: Optimal zone for bandwidth selection in semiparametric models Abstract: We study the general problem of bandwidth selection in semiparametric regression. By expanding the higher-order terms in the Taylor series for the asymptotic mean-squared error, we provide a theoretical justification for the earlier empirical observations of an optimal zone of bandwidths in the literature. Based on the idea of cross-validating parametrical estimates, we further introduce a novel bandwidth selector for semiparametric models. The method is demonstrated by numerical studies to be able to preserve the selected bandwidth within the optimal zone. This data-driven cross-validation method may also be applicable for model diagnosis and longitudinal data settings. Examples from two clinical trials are provided to illustrate the applications. Journal: Journal of Nonparametric Statistics Pages: 701-717 Issue: 3 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.533768 File-URL: http://hdl.handle.net/10.1080/10485252.2010.533768 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:701-717 Template-Type: ReDIF-Article 1.0 Author-Name: W. Lok Author-X-Name-First: W. Author-X-Name-Last: Lok Author-Name: Stephen Lee Author-X-Name-First: Stephen Author-X-Name-Last: Lee Title: A new statistical depth function with applications to multimodal data Abstract: We propose a new statistical depth function based on interpoint distances, which has the distinct property of respecting multimodality in data configurations. This property proves to be especially relevant to many inference problems including confidence region construction, classification, tests for equality of populations, p-value computation, etc. With specification of an appropriate interpoint distance, our depth function also applies to infinite-dimensional data. A number of examples are used to illustrate the diverse applicability of our proposed depth function in different problem settings, where the conventional centre-outward ordering depth functions are found to be inadequate. Journal: Journal of Nonparametric Statistics Pages: 617-631 Issue: 3 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.553953 File-URL: http://hdl.handle.net/10.1080/10485252.2011.553953 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:617-631 Template-Type: ReDIF-Article 1.0 Author-Name: Samis Trevezas Author-X-Name-First: Samis Author-X-Name-Last: Trevezas Author-Name: Nikolaos Limnios Author-X-Name-First: Nikolaos Author-X-Name-Last: Limnios Title: Exact MLE and asymptotic properties for nonparametric semi-Markov models Abstract: This article concerns maximum-likelihood estimation for discrete time homogeneous nonparametric semi-Markov models with finite state space. In particular, we present the exact maximum-likelihood estimator of the semi-Markov kernel which governs the evolution of the semi-Markov chain (SMC). We study its asymptotic properties in the following cases: (i) for one observed trajectory, when the length of the observation tends to infinity, and (ii) for parallel observations of independent copies of an SMC censored at a fixed time, when the number of copies tends to infinity. In both cases, we obtain strong consistency, asymptotic normality, and asymptotic efficiency for every finite dimensional vector of this estimator. Finally, we obtain explicit forms for the covariance matrices of the asymptotic distributions. Journal: Journal of Nonparametric Statistics Pages: 719-739 Issue: 3 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.555543 File-URL: http://hdl.handle.net/10.1080/10485252.2011.555543 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:719-739 Template-Type: ReDIF-Article 1.0 Author-Name: Tae Kim Author-X-Name-First: Tae Author-X-Name-Last: Kim Author-Name: Zhi-Ming Luo Author-X-Name-First: Zhi-Ming Author-X-Name-Last: Luo Author-Name: Chiho Kim Author-X-Name-First: Chiho Author-X-Name-Last: Kim Title: The central limit theorem for degenerate variable -statistics under dependence Abstract: The central limit theorem (CLT) for degenerate U-statistics with a variable symmetric kernel function has been studied under dependence by many authors, since it has many important applications in nonparametric estimation and testing problems [see, e.g. Takahata, H., and Yoshihara, K. (1987), ‘Central Limit Theorems for Integrated Square Error of Nonparametric Density Estimators Based on a Absolutely Regular Random Sequences’, Yokohama Mathematical Journal, 35, 95–111; Yoshihara, K. (1989), ‘Limiting Behavior of Generalized Quadratic Forms Generated by Absolutely Regular Sequences II’, Yokohama Mathematical Journal, 37, 109–123. Yoshihara, K. (1992), ‘Limiting Behavior of Generalized Quadratic Forms Generated by Absolutely Regular Sequences III’, Yokohama Mathematical Journal, 40, 1–9; Fan, J., and Li, Q. (1999), ‘Central Limit Theorem for Degenerate U-Statistics of Absolutely Regular Processes with Applications to Model Specification Testing’, Journal of Nonparametric Statistics, 10, 245–271; Gao, J., and King, M.L. (2004), ‘Adaptive Testing in Continuous-time Diffusion Models’, Econometric Theory, 20, 844–882; Gao, J. (2007), Nonlinear Time Series: Semiparametric and Nonparametric Methods, Chapman & Hall/CRC; Gao, J., and Hong, Y. (2008), ‘Central Limit Theorem for Generalized U-statistics with Applications in Nonparametric Specification’, Journal of Nonparametric Statistics, 20, 61–76]. In this paper, we provide an improved version with the asymmetric kernel method which is quite useful for application to nonparametric methods in various situations. As an illustration of the usefulness of our result, CLTs for quadratic errors of a nonparametric density estimator are developed under dependency, which is meaningful in its own right. Journal: Journal of Nonparametric Statistics Pages: 683-699 Issue: 3 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.556193 File-URL: http://hdl.handle.net/10.1080/10485252.2011.556193 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:683-699 Template-Type: ReDIF-Article 1.0 Author-Name: Narayanaswamy Balakrishnan Author-X-Name-First: Narayanaswamy Author-X-Name-Last: Balakrishnan Author-Name: Hon Ng Author-X-Name-First: Hon Author-X-Name-Last: Ng Author-Name: Jorge Navarro Author-X-Name-First: Jorge Author-X-Name-Last: Navarro Title: Exact nonparametric inference for component lifetime distribution based on lifetime data from systems with known signatures Abstract: In this paper, we develop exact nonparametric statistical inference for some characteristics of the component lifetime distribution based on the lifetimes of coherent systems with known signatures. Distribution-free confidence limits for population quantiles of component lifetime distributions are derived. Computational formulas as well as a procedure for choosing suitable confidence limits are presented. Construction of tolerance limits for the component lifetime distribution is also described. Finally, some examples are presented to illustrate the methods of inference developed here. Journal: Journal of Nonparametric Statistics Pages: 741-752 Issue: 3 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.559547 File-URL: http://hdl.handle.net/10.1080/10485252.2011.559547 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:741-752 Template-Type: ReDIF-Article 1.0 Author-Name: Zhong Guan Author-X-Name-First: Zhong Author-X-Name-Last: Guan Author-Name: Cheng Peng Author-X-Name-First: Cheng Author-X-Name-Last: Peng Title: A rank-based empirical likelihood approach to two-sample proportional odds model and its goodness of fit Abstract: A rank-based empirical likelihood method is proposed and applied to estimate the proportionality parameter and the underlying distributions in a two-sample semiparametric proportional odds model. A distribution-free goodness-of-fit test for the model is also given. It is proved that the maximum likelihood estimator of the proportionality parameter is reciprocal symmetric. As one of the applications, we use the proposed procedure to estimate receiver operating characteristic (ROC) curves. We also perform a simulation study to assess the performance of the proposed procedure and provide a numerical example based on real-world data to illustrate the implementation of the method. Journal: Journal of Nonparametric Statistics Pages: 763-780 Issue: 3 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.559726 File-URL: http://hdl.handle.net/10.1080/10485252.2011.559726 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:763-780 Template-Type: ReDIF-Article 1.0 Author-Name: F. Giordano Author-X-Name-First: F. Author-X-Name-Last: Giordano Author-Name: M. La Rocca Author-X-Name-First: M. Author-X-Name-Last: La Rocca Author-Name: C. Perna Author-X-Name-First: C. Author-X-Name-Last: Perna Title: Properties of the neural network sieve bootstrap Abstract: In this paper, a sieve bootstrap scheme, the neural network sieve bootstrap, for nonlinear time series is proposed. The approach, which is nonparametric in its spirit, retains the conceptual simplicity of a classical residual bootstrap, and it has some advantages with respect to the blockwise schemes and kernel bootstrap techniques. The resampling scheme from the residuals of the feedforward neural networks is shown to be asymptotically justified. A Monte Carlo simulation study shows that the procedure performs similar to the autoregressive (AR)-sieve bootstrap for linear processes, while it outperforms the AR-sieve bootstrap, the moving block bootstrap and kernel bootstrap for nonlinear processes, both in terms of bias and variability. Journal: Journal of Nonparametric Statistics Pages: 803-817 Issue: 3 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.561344 File-URL: http://hdl.handle.net/10.1080/10485252.2011.561344 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:803-817 Template-Type: ReDIF-Article 1.0 Author-Name: Pao-Sheng Shen Author-X-Name-First: Pao-Sheng Author-X-Name-Last: Shen Title: Testing quasi-independence for doubly truncated data Abstract: Doubly truncated data appear in a number of applications, including astronomy and survival analysis. Quasi-independence is a common assumption for analysing double-truncated data. To verify this condition, using the approach of Emura and Wang [(2010), ‘Testing Quasi-independence for Truncation Data’, Journal of Multivariate Analysis, 101, 223–293], we propose a class of weighted log-rank-type statistics. The asymptotic distribution theory of the test is presented. The performance of the proposed test is compared with the existing test proposed by Martin and Betensky [(2005), ‘Testing Quasi-independence of Failure and Truncation Via Conditional Kendall's Tau’, Journal of the American Statistical Association, 100, 484–492], by means of Monte Carlo simulations. Journal: Journal of Nonparametric Statistics Pages: 753-761 Issue: 3 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.564280 File-URL: http://hdl.handle.net/10.1080/10485252.2011.564280 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:753-761 Template-Type: ReDIF-Article 1.0 Author-Name: Hugo Harari-Kermadec Author-X-Name-First: Hugo Author-X-Name-Last: Harari-Kermadec Title: Regenerative block empirical likelihood for Markov chains Abstract: Empirical likelihood (EL) is a powerful semi-parametric method increasingly investigated in the literature. However, most authors essentially focus on an i.i.d. setting. In the case of dependent data, the classical EL method cannot be directly applied on the data but rather on blocks of consecutive data catching the dependence structure. Generalisation of EL based on the construction of blocks of increasing random length have been proposed for time series satisfying mixing conditions. Following some recent developments in the bootstrap literature, we propose a generalisation for a large class of Markov chains, based on small blocks of various lengths. Our approach makes use of the regenerative structure of Markov chains, which allows us to construct blocks which are almost independent (independent in the atomic case). We obtain the asymptotic validity of the method for positive recurrent Markov chains and present some simulation results. Journal: Journal of Nonparametric Statistics Pages: 781-802 Issue: 3 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.565340 File-URL: http://hdl.handle.net/10.1080/10485252.2011.565340 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:781-802 Template-Type: ReDIF-Article 1.0 Author-Name: Yongsong Qin Author-X-Name-First: Yongsong Author-X-Name-Last: Qin Author-Name: Yinghua Li Author-X-Name-First: Yinghua Author-X-Name-Last: Li Author-Name: Weizhen Yang Author-X-Name-First: Weizhen Author-X-Name-Last: Yang Author-Name: Qingzhu Lei Author-X-Name-First: Qingzhu Author-X-Name-Last: Lei Title: Confidence intervals for nonparametric regression functions under negatively associated errors Abstract: In this paper, we study the construction of confidence intervals for a nonparametric regression function under a negatively associated sample by using the blockwise technique. It is shown that the blockwise empirical likelihood (EL) ratio statistic is asymptotically χ2 distributed. The result is used to obtain EL-based confidence intervals for a nonparametric regression function. The results of a simulation study on the finite sample performance of the proposed confidence intervals are reported. Journal: Journal of Nonparametric Statistics Pages: 645-659 Issue: 3 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.566335 File-URL: http://hdl.handle.net/10.1080/10485252.2011.566335 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:645-659 Template-Type: ReDIF-Article 1.0 Author-Name: Alain Berlinet Author-X-Name-First: Alain Author-X-Name-Last: Berlinet Author-Name: Rémi Servien Author-X-Name-First: Rémi Author-X-Name-Last: Servien Title: Necessary and sufficient condition for the existence of a limit distribution of the nearest-neighbour density estimator Abstract: Many convergence results in density estimation can be stated without any restriction on the function to be estimated. Unlike these universal properties, the asymptotic normality of estimators often requires hypotheses on the derivatives of the underlying density and additional conditions on the smoothing parameter. Yet, despite the possible bad local behaviour of the density (it is not continuous or has infinite derivative), the convergence in law of the nearest-neighbour estimator still may occur and provide confidence bands for the estimated density. Therefore, a natural question arises: Is it possible to get a necessary and sufficient condition for the existence of a limit distribution of the nearest-neighbour estimator? We answer this question by using the regularity index recently introduced by Beirlant, Berlinet and Biau [(2008), ‘Higher Order Estimation at Lebesgue Points’, Annals of the Institute of Statistical Mathematics, 60, 651–677]. As expected, when it does exist, the limit distribution is Gaussian. Its mean and variance are explicitly given as functions of the regularity index. The second-order term in the expansion of the small ball probability is shown to be the crucial parameter. In contrast to the former results on sufficiency of conditions for asymptotic normality, no continuity hypothesis is required for the underlying density. Journal: Journal of Nonparametric Statistics Pages: 633-643 Issue: 3 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.567334 File-URL: http://hdl.handle.net/10.1080/10485252.2011.567334 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:633-643 Template-Type: ReDIF-Article 1.0 Author-Name: A. Saleh Author-X-Name-First: A. Author-X-Name-Last: Saleh Author-Name: B. Golam Kibria Author-X-Name-First: B. Author-X-Name-Last: Golam Kibria Title: On some ridge regression estimators: a nonparametric approach Abstract: This paper considers the R-estimation of the parameters of a multiple regression model when the design matrix is ill-conditioned. Accordingly, we introduce the ridge regression (RR) modification to the usual R-estimators and consider five RR R-estimators when it is suspected that the regression parameters may belong to a linear subspace of the parameter space. The regions of optimality of the proposed estimators are determined based on the quadratic risks. Asymptotic relative efficiency tables and risk graphs are provided for the numerical and graphical comparisons of the five estimators. Journal: Journal of Nonparametric Statistics Pages: 819-851 Issue: 3 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.567335 File-URL: http://hdl.handle.net/10.1080/10485252.2011.567335 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:819-851 Template-Type: ReDIF-Article 1.0 Author-Name: Kaushik Ghosh Author-X-Name-First: Kaushik Author-X-Name-Last: Ghosh Author-Name: Ram Tiwari Author-X-Name-First: Ram Author-X-Name-Last: Tiwari Title: A unified approach to variations of ranked set sampling with applications Abstract: In this article, we develop a general theory of inference using data collected from different variations of ranked set sampling. Such variations include balanced and unbalanced ranked set sampling, balanced and unbalanced k-tuple ranked set sampling, nomination sampling, simple random sampling, as well as a combination of them. We provide methods of estimating the underlying distribution function as well as its functionals and establish the asymptotic properties of the resulting estimators. The results so obtained can be used to develop nonparametric procedures for one- and two-sample problems. Some investigation of the small-sample properties of these estimators is also provided. We conclude with an application to a real-life example. Journal: Journal of Nonparametric Statistics Pages: 471-485 Issue: 4 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802652077 File-URL: http://hdl.handle.net/10.1080/10485250802652077 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:4:p:471-485 Template-Type: ReDIF-Article 1.0 Author-Name: Juan Mora Author-X-Name-First: Juan Author-X-Name-Last: Mora Author-Name: Alicia Pérez-Alonso Author-X-Name-First: Alicia Author-X-Name-Last: Pérez-Alonso Title: Specification tests for the distribution of errors in nonparametric regression: a martingale approach Abstract: We discuss how to test whether the distribution of regression errors belongs to a parametric family of continuous distribution functions, making no parametric assumption about the conditional mean or the conditional variance in the regression model. We propose using test statistics that are based on a martingale transform of the estimated empirical process. We prove that these statistics are asymptotically distribution-free, and two Monte Carlo experiments show that they work reasonably well in practice. Journal: Journal of Nonparametric Statistics Pages: 441-452 Issue: 4 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802666192 File-URL: http://hdl.handle.net/10.1080/10485250802666192 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:4:p:441-452 Template-Type: ReDIF-Article 1.0 Author-Name: Florent Burba Author-X-Name-First: Florent Author-X-Name-Last: Burba Author-Name: Frédéric Ferraty Author-X-Name-First: Frédéric Author-X-Name-Last: Ferraty Author-Name: Philippe Vieu Author-X-Name-First: Philippe Author-X-Name-Last: Vieu Title: -Nearest Neighbour method in functional nonparametric regression Abstract: The aim of this article is to study the k-nearest neighbour (kNN) method in nonparametric functional regression. We present asymptotic properties of the kNN kernel estimator: the almost-complete convergence and its rate. Then, we illustrate the effectiveness of this method by comparing it with the traditional kernel approach first on simulated datasets and then on a real chemometrical example. We also present in this article an important technical tool which could be useful in many other situations than ours. Journal: Journal of Nonparametric Statistics Pages: 453-469 Issue: 4 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250802668909 File-URL: http://hdl.handle.net/10.1080/10485250802668909 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:4:p:453-469 Template-Type: ReDIF-Article 1.0 Author-Name: Wang-Li Xu Author-X-Name-First: Wang-Li Author-X-Name-Last: Xu Author-Name: Li-Xing Zhu Author-X-Name-First: Li-Xing Author-X-Name-Last: Zhu Title: A goodness-of-fit test for a varying-coefficients model in longitudinal studies Abstract: In this paper, we construct an empirical process-based test to examine the adequacy of a varying-coefficient model. A Monte Carlo approach is applied to approximate the null distribution of the test. Beyond the desired features that are shared by the existing empirical process-based tests, the Monte Carlo approximation makes the test self-invariant such that studentisation for the test statistic is not needed. Thus, the variance of residuals, as a studentising constant that is model dependent and may deteriorate the power of test, is no need to estimate. Simulations and an example are provided to illustrate our methodology. Journal: Journal of Nonparametric Statistics Pages: 427-440 Issue: 4 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902721806 File-URL: http://hdl.handle.net/10.1080/10485250902721806 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:4:p:427-440 Template-Type: ReDIF-Article 1.0 Author-Name: Hanna Jankowski Author-X-Name-First: Hanna Author-X-Name-Last: Jankowski Author-Name: Jon Wellner Author-X-Name-First: Jon Author-X-Name-Last: Wellner Title: Computation of nonparametric convex hazard estimators via profile methods Abstract: This paper proposes a profile likelihood algorithm to compute the nonparametric maximum likelihood estimator of a convex hazard function. The maximisation is performed in two steps: First the support reduction algorithm is used to maximise the likelihood over all hazard functions with a given point of minimum (or antimode). Then it is shown that the profile (or partially maximised) likelihood is quasi-concave as a function of the antimode, so that a bisection algorithm can be applied to find the maximum of the profile likelihood, and hence also the global maximum. The new algorithm is illustrated using both artificial and real data, including lifetime data for Canadian males and females. Journal: Journal of Nonparametric Statistics Pages: 505-518 Issue: 4 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902745359 File-URL: http://hdl.handle.net/10.1080/10485250902745359 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:4:p:505-518 Template-Type: ReDIF-Article 1.0 Author-Name: Li Wang Author-X-Name-First: Li Author-X-Name-Last: Wang Title: Single-index model-assisted estimation in survey sampling Abstract: A model-assisted semiparametric method of estimating finite-population totals is investigated to improve the precision of survey estimators by incorporating multivariate auxiliary information. The proposed superpopulation model is a single-index model (SIM) which has proven to be a simple and efficient semiparametric tool in multivariate regression. A class of estimators based on polynomial spline regression is proposed. These estimators are robust against deviation from SIMs. Under standard design conditions, the proposed estimators are asymptotically design-unbiased, consistent and asymptotically normal. An iterative optimisation routine is provided that is sufficiently fast for users to analyze large and complex survey data within seconds. The proposed method has been applied to simulated datasets and MU281 dataset, which have provided strong evidence that corroborates with the asymptotic theory. Journal: Journal of Nonparametric Statistics Pages: 487-504 Issue: 4 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902773849 File-URL: http://hdl.handle.net/10.1080/10485250902773849 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:4:p:487-504 Template-Type: ReDIF-Article 1.0 Author-Name: Wojciech Maciak Author-X-Name-First: Wojciech Author-X-Name-Last: Maciak Title: Exact null distribution for ≤25 and probability approximations for Spearman's score in an absence of ties Journal: Pages: 519-519 Issue: 4 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902797152 File-URL: http://hdl.handle.net/10.1080/10485250902797152 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:4:p:519-519 Template-Type: ReDIF-Article 1.0 Author-Name: Erich Lehmann Author-X-Name-First: Erich Author-X-Name-Last: Lehmann Title: Parametric versus nonparametrics: two alternative methodologies Abstract: This article compares parametric and nonparametric approaches to statistical inference. It considers their advantages and disadvantages, and their areas of applicability. Although there is no clear comprehensive conclusion, the article finds that in simple problems in which Wilcoxon type tests and estimators apply, they may be recommended as the methods of choice. Journal: Journal of Nonparametric Statistics Pages: 397-405 Issue: 4 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902842727 File-URL: http://hdl.handle.net/10.1080/10485250902842727 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:4:p:397-405 Template-Type: ReDIF-Article 1.0 Author-Name: R. Eubank Author-X-Name-First: R. Author-X-Name-Last: Eubank Title: Comment on ‘Parametric versus nonparametrics: two alternative methodologies’ Journal: Journal of Nonparametric Statistics Pages: 407-410 Issue: 4 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902844707 File-URL: http://hdl.handle.net/10.1080/10485250902844707 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:4:p:407-410 Template-Type: ReDIF-Article 1.0 Author-Name: Jeffrey Hart Author-X-Name-First: Jeffrey Author-X-Name-Last: Hart Title: Discussion of ‘Parametric versus nonparametrics: two alternative methodologies’ Journal: Journal of Nonparametric Statistics Pages: 411-413 Issue: 4 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902846835 File-URL: http://hdl.handle.net/10.1080/10485250902846835 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:4:p:411-413 Template-Type: ReDIF-Article 1.0 Author-Name: Xihong Lin Author-X-Name-First: Xihong Author-X-Name-Last: Lin Author-Name: Lee Dicker Author-X-Name-First: Lee Author-X-Name-Last: Dicker Title: Discussion of ‘Parametric versus nonparametrics: two alternative methdologies’ Journal: Journal of Nonparametric Statistics Pages: 415-417 Issue: 4 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902846868 File-URL: http://hdl.handle.net/10.1080/10485250902846868 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:4:p:415-417 Template-Type: ReDIF-Article 1.0 Author-Name: Joseph Romano Author-X-Name-First: Joseph Author-X-Name-Last: Romano Title: Discussion of ‘Parametric versus nonparametrics: two alternative methodologies’ Journal: Journal of Nonparametric Statistics Pages: 419-424 Issue: 4 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902846900 File-URL: http://hdl.handle.net/10.1080/10485250902846900 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:4:p:419-424 Template-Type: ReDIF-Article 1.0 Author-Name: Erich Lehmann Author-X-Name-First: Erich Author-X-Name-Last: Lehmann Title: Rejoinder Abstract: I am grateful to the four discussants for their interesting and helpful comments. Their contributions have a common structure. They take cognisance of the narrow focus of my survey, and discuss various aspects and issues that I did not cover. Let me be more specific. Journal: Journal of Nonparametric Statistics Pages: 425-426 Issue: 4 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902846926 File-URL: http://hdl.handle.net/10.1080/10485250902846926 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:4:p:425-426 Template-Type: ReDIF-Article 1.0 Author-Name: Shuran Zhao Author-X-Name-First: Shuran Author-X-Name-Last: Zhao Author-Name: Xingzhong Xu Author-X-Name-First: Xingzhong Author-X-Name-Last: Xu Author-Name: Xiaobo Ding Author-X-Name-First: Xiaobo Author-X-Name-Last: Ding Title: The convergence rates of the weighted bootstrap distributions for von Mises and -statistics Abstract: It has been proved that the weighted bootstrap method for von Mises and U-statistics provides a feasible approximation to their sample distributions. In the paper, based on a variation of the Berry-Esseen theorem for U-statistics, we further develop such first-order convergence rate under weak conditions. Moreover, in view of maximum entropy, we provide a principle to choose the weights. Journal: Journal of Nonparametric Statistics Pages: 645-660 Issue: 7 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802280259 File-URL: http://hdl.handle.net/10.1080/10485250802280259 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:7:p:645-660 Template-Type: ReDIF-Article 1.0 Author-Name: Taoufik Bouezmarni Author-X-Name-First: Taoufik Author-X-Name-Last: Bouezmarni Author-Name: Jeroen Rombouts Author-X-Name-First: Jeroen Author-X-Name-Last: Rombouts Title: Density and hazard rate estimation for censored and α-mixing data using gamma kernels Abstract: In this paper, we consider the non-parametric estimation for a density and hazard rate function for right censored α-mixing survival time data using kernel smoothing techniques. As survival times are positive with potentially high concentration at zero, one has to take into account the bias problems when the functions are estimated in the boundary region. In this paper, gamma kernel estimators of the density and the hazard rate function are proposed. The estimators use adaptive weights depending on the point in which we estimate the function, and they are robust to the boundary bias problem. For both estimators, the mean-squared error properties, including the rate of convergence, the almost sure consistency, and the asymptotic normality, are investigated. The results of a simulation study demonstrate the performance of the proposed estimators. Journal: Journal of Nonparametric Statistics Pages: 627-643 Issue: 7 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802290670 File-URL: http://hdl.handle.net/10.1080/10485250802290670 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:7:p:627-643 Template-Type: ReDIF-Article 1.0 Author-Name: C. Crambes Author-X-Name-First: C. Author-X-Name-Last: Crambes Author-Name: L. Delsol Author-X-Name-First: L. Author-X-Name-Last: Delsol Author-Name: A. Laksaci Author-X-Name-First: A. Author-X-Name-Last: Laksaci Title: Robust nonparametric estimation for functional data Abstract: Robust estimation provides an alternative approach to classical methods, for instance, when the data are affected by the presence of outliers. Recently, these robust estimators have been considered for models with functional data. In this paper, we focus on asymptotic properties of a conditional nonparametric estimation of a real-valued variable with a functional covariate. We present results dealing with 𝕃q errors of these estimators. Then, our estimation procedure is evaluated by means of some applications to real data sets. Journal: Journal of Nonparametric Statistics Pages: 573-598 Issue: 7 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802331524 File-URL: http://hdl.handle.net/10.1080/10485250802331524 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:7:p:573-598 Template-Type: ReDIF-Article 1.0 Author-Name: Nicoleta Serban Author-X-Name-First: Nicoleta Author-X-Name-Last: Serban Title: Estimating and clustering curves in the presence of heteroscedastic errors Abstract: The technique introduced in this paper is a means for estimating and discovering underlying patterns for a large number of curves observed with heteroscedastic errors. Therefore, both the mean and the variance functions of each curve are assumed unknown and varying over time. The method consists of a series of steps. We transform using an orthonormal basis of functions in L2. In the transform domain, the non-parametric regression is reduced to a means model. To estimate the means in the transform domain, we consider the class of linear or modulation estimators and proceed as in Beran and Dümbgen (R. Beran and L. Dümbgen, Modulation of estimators and confidence sets, Ann. Stat. 26(5) (1998), pp. 1826–1856.) by minimising the Stein's unbiased risk estimate. By minimising the risk over a nested subset selection of modulators, we reduce the dimensionality of the means space. We show that in the transform space, the risk estimate is asymptotically optimal in the Pinsker's minimax sense over Sobolev ellipsoids under heteroscedastic errors. Coefficient estimation and dimensionality reduction via optimal risk estimation is essential for accurate clustering membership estimation. We illustrate our technique by estimating and clustering a large number of curves both within a synthetic example and within a specific application. In this application, we analyse the research and development expenditure of a subset of companies in the Compustat Global database. We show that our method compares favourably to two alternative approaches. Journal: Journal of Nonparametric Statistics Pages: 553-571 Issue: 7 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802348742 File-URL: http://hdl.handle.net/10.1080/10485250802348742 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:7:p:553-571 Template-Type: ReDIF-Article 1.0 Author-Name: Thoralf Mildenberger Author-X-Name-First: Thoralf Author-X-Name-Last: Mildenberger Title: A geometric interpretation of the multiresolution criterion in nonparametric regression Abstract: A recent approach to choosing the amount of smoothing in nonparametric regression is to select the simplest estimate for which the residuals ‘look like white noise’. This can be checked with the so-called multiresolution criterion, which Davies and Kovac [P.L. Davies and A. Kovac, Local extremes, runs, strings and multiresolutions (with discussion and rejoinder), Ann. Stat. 29 (2001), pp. 1–65.] introduced in connection with their taut-string procedure. It has also been used in several other nonparametric procedures such as spline smoothing or piecewise constant regression. We show that this criterion is related to a norm, the multiresolution norm (MR-norm). We point out some important differences between this norm and p-norms. The MR-norm is not invariant w.r.t. sign changes and permutations, and this makes it useful for detecting runs of residuals of the same sign. We also give sharp upper and lower bounds for the MR-norm in terms of p-norms. Journal: Journal of Nonparametric Statistics Pages: 599-609 Issue: 7 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802360994 File-URL: http://hdl.handle.net/10.1080/10485250802360994 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:7:p:599-609 Template-Type: ReDIF-Article 1.0 Author-Name: Tang Qingguo Author-X-Name-First: Tang Author-X-Name-Last: Qingguo Author-Name: Cheng Longsheng Author-X-Name-First: Cheng Author-X-Name-Last: Longsheng Title: M-estimation and B-spline approximation for varying coefficient models with longitudinal data Abstract: A global smoothing procedure is developed using B-spline function approximations for estimating the unknown functions of a varying coefficient model with repeated measurements. A general formulation is used to treat mean, median, quantile and robust mean regressions in one setting. The global convergence rates of the M-estimators of unknown coefficient functions are established. The asymptotic distributes of M-estimators are derived and the approximate confidence intervals are also established. Various applications of the main results, including estimating conditional quantile coefficient functions and robustifying the mean regression coefficient functions are given. Finite sample properties of our procedures are studied through Monte Carlo simulations. Journal: Journal of Nonparametric Statistics Pages: 611-625 Issue: 7 Volume: 20 Year: 2008 X-DOI: 10.1080/10485250802375950 File-URL: http://hdl.handle.net/10.1080/10485250802375950 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:20:y:2008:i:7:p:611-625 Template-Type: ReDIF-Article 1.0 Author-Name: Mihee Lee Author-X-Name-First: Mihee Author-X-Name-Last: Lee Author-Name: Haipeng Shen Author-X-Name-First: Haipeng Author-X-Name-Last: Shen Author-Name: Christina Burch Author-X-Name-First: Christina Author-X-Name-Last: Burch Author-Name: J. Marron Author-X-Name-First: J. Author-X-Name-Last: Marron Title: Direct deconvolution density estimation of a mixture distribution motivated by mutation effects distribution Abstract: The mutation effect distribution is essential for understanding evolutionary dynamics. However, the existing studies on this problem have had limited resolution. So far, the most widely used method is to fit some parametric distribution, such as an exponential distribution whose validity has not been checked. In this paper, we propose a nonparametric density estimator for the mutation effect distribution, based on a deconvolution approach. Consistency of the estimator is also established. Unlike the existing deconvolution estimators, we cover the case that the target variable has a mixture structure with a pointmass and a continuous component. To study the property of the proposed estimator, several simulation studies are performed. In addition, an application for modelling virus mutation effects is provided. Journal: Journal of Nonparametric Statistics Pages: 1-22 Issue: 1 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903085847 File-URL: http://hdl.handle.net/10.1080/10485250903085847 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:1:p:1-22 Template-Type: ReDIF-Article 1.0 Author-Name: Albert Vexler Author-X-Name-First: Albert Author-X-Name-Last: Vexler Author-Name: Aiyi Liu Author-X-Name-First: Aiyi Author-X-Name-Last: Liu Author-Name: Enrique Schisterman Author-X-Name-First: Enrique Author-X-Name-Last: Schisterman Title: Nonparametric deconvolution of density estimation based on observed sums Abstract: This paper develops a methodology for distribution-free estimation of a density function based on observed sums or pooled data. The proposed methods employ a Fourier approach to nonparametric deconvolution of a density estimate. Asymptotic normality is established and an upper bound for the integrated absolute error is given for the proposed density estimator. Monte Carlo simulations are used to examine the performance of the density estimators. The proposed techniques are exemplified using data from a study of biomarkers associated with coronary heart disease. Journal: Journal of Nonparametric Statistics Pages: 23-39 Issue: 1 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903094286 File-URL: http://hdl.handle.net/10.1080/10485250903094286 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:1:p:23-39 Template-Type: ReDIF-Article 1.0 Author-Name: Didier Girard Author-X-Name-First: Didier Author-X-Name-Last: Girard Title: Estimating the accuracy of (local) cross-validation via randomised GCV choices in kernel or smoothing spline regression Abstract: In nonparametric regression, it is generally crucial to select ‘nearly’ optimal smoothing parameters for which the underlying average squared error (Δ ), with given weights, is ‘nearly’ minimised. The cross-validation (CV) selector or the GCV selector are popular for this task, but it has been observed by many statisticians that these selectors may happen to be ‘not sufficiently’ accurate in some situations. So a practical matter of great importance is the development of reliable estimates of this accuracy. The purpose of this paper is to show that the simulation of the randomised GCV selector or a simple general variant using an ‘augmented-randomised-trace’, can provide useful inferences, like consistent estimates of the standard error in the CV selector or of the expected increase of Δ due to this error. Furthermore, this also provides a tool for constructing more parsimonious curve estimates having almost the same asymptotic justification as the CV estimate, namely with similar increase of Δ up to a given factor. Rigorous proofs are given in the context of one-dimensional kernel regression. Simulated examples, also in this context, illustrate the usefulness of the methodology even at moderate sample sizes. Some direct extensions (for multi-dimensional kernels, equispaced splines) of the theoretical results are outlined. We give heuristics which indicate that the general methodology proposed in this article should be useful in many curve-, surface- or image-estimation problems when using spline-like smoothers. Journal: Journal of Nonparametric Statistics Pages: 41-64 Issue: 1 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903095820 File-URL: http://hdl.handle.net/10.1080/10485250903095820 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:1:p:41-64 Template-Type: ReDIF-Article 1.0 Author-Name: Stephen Portnoy Author-X-Name-First: Stephen Author-X-Name-Last: Portnoy Author-Name: Guixian Lin Author-X-Name-First: Guixian Author-X-Name-Last: Lin Title: Asymptotics for censored regression quantiles Abstract: It has been difficult to generalise Kaplan–Meier approaches to censored regression data under the minimal condition that censoring and response are conditionally independent given the explanatory variables. Portnoy [S. Portnoy, Censored regression quantiles, J. Am. Stat. Assoc. 98 (2003), pp. 1001–1012.] provided such a generalisation based on the paradigm of censored quantile regression. However, previous research has only provided consistency results for this approach. The results here provide an asymptotic distribution theory under relatively mild conditions for a gridded version of the algorithm in Portnoy [S. Portnoy, Censored regression quantiles, J. Am. Stat. Assoc. 98 (2003), pp. 1001–1012.], and show that the asymptotics for censored regression quantiles are an exact generalisation of those for the Kaplan–Meier estimator in one sample. Journal: Journal of Nonparametric Statistics Pages: 115-130 Issue: 1 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903105009 File-URL: http://hdl.handle.net/10.1080/10485250903105009 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:1:p:115-130 Template-Type: ReDIF-Article 1.0 Author-Name: Barbara Wieczorek Author-X-Name-First: Barbara Author-X-Name-Last: Wieczorek Title: On optimal estimation of the mode in nonparametric deconvolution problems Abstract: This work deals with the problem of estimating the mode in nonparametric deconvolution models. First, given n i.i.d. observations from Y=X+ϵ, we consider estimating the mode θ of a density function of some random variable X. Second, we consider the errors-in-variables regression model, where we are interested in the mode of m(x)=E(Z|X=x), where n i.i.d. observations from (Y, Z) with Y=X+ϵ are given. In both cases, we assume the distribution of ϵ to be ordinary smooth. The mode estimator ˆθn is defined via maximising over a curve estimator of the kernel type. In both deconvolution models, we obtain rates for the quadratic risk of ˆθn, depending on the smoothness of the underlying curve and the degree of ill-posedness of the deconvolution problem. Further, we show that these rates are optimal, considering one-dimensional subproblems in the class of functions studied. Journal: Journal of Nonparametric Statistics Pages: 65-80 Issue: 1 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903121626 File-URL: http://hdl.handle.net/10.1080/10485250903121626 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:1:p:65-80 Template-Type: ReDIF-Article 1.0 Author-Name: Shunpu Zhang Author-X-Name-First: Shunpu Author-X-Name-Last: Zhang Author-Name: Rohana Karunamuni Author-X-Name-First: Rohana Author-X-Name-Last: Karunamuni Title: Boundary performance of the beta kernel estimators Abstract: The beta kernel estimators are shown in Chen [S.X. Chen, Beta kernel estimators for density functions, Comput. Statist. Data Anal. 31 (1999), pp. 131–145] to be non-negative and have less severe boundary problems than the conventional kernel estimator. Numerical results in Chen [S.X. Chen, Beta kernel estimators for density functions, Comput. Statist. Data Anal. 31 (1999), pp. 131–145] further show that beta kernel estimators have better finite sample performance than some of the widely used boundary corrected estimators. However, our study finds that the numerical comparisons of Chen are confounded with the choice of the bandwidths and the quantities being compared. In this paper, we show that the performances of the beta kernel estimators are very similar to that of the reflection estimator, which does not have the boundary problem only for densities exhibiting a shoulder at the endpoints of the support. For densities not exhibiting a shoulder, we show that the beta kernel estimators have a serious boundary problem and their performances at the boundary are inferior to that of the well-known boundary kernel estimator. Journal: Journal of Nonparametric Statistics Pages: 81-104 Issue: 1 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903124984 File-URL: http://hdl.handle.net/10.1080/10485250903124984 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:1:p:81-104 Template-Type: ReDIF-Article 1.0 Author-Name: J. Liao Author-X-Name-First: J. Author-X-Name-Last: Liao Author-Name: Yujun Wu Author-X-Name-First: Yujun Author-X-Name-Last: Wu Author-Name: Yong Lin Author-X-Name-First: Yong Author-X-Name-Last: Lin Title: Improving Sheather and Jones’ bandwidth selector for difficult densities in kernel density estimation Abstract: Kernel density estimation is a widely used statistical tool and bandwidth selection is critically important. The Sheather and Jones’ (SJ) selector [A reliable data-based bandwidth selection method for kernel density estimation, J. R. Stat. Soc. Ser. B 53 (1991), pp. 683–690] remains the best available data-driven bandwidth selector. It can, however, perform poorly if the true density deviates too much in shape from normal. This paper first develops an alternative selector by following ideas in Park and Marron [On the use of pilot estimators in bandwidth selection, Nonparametr. Stat. 1 (1992), pp. 231–240] to reduce the impact of the normal reference density. The selector can bring drastic improvement to less smooth densities that the SJ selector has difficulty with, but may be slightly worse off otherwise. We then propose to combine the alternative selector and SJ selector by using the smaller of the two bandwidths, which has the effect of automatically picking the better one for a particular density. In our extensive simulation, study using the 15 benchmark densities in Marron and Wand [Exact mean integrated squared error, Ann. Statist. 20 (1992), pp. 712–736], the combined selector significantly improves the SJ selector for 5 difficult densities and retains the superior performance of the SJ selector for the other 10. A ready-to-use R function is provided. Journal: Journal of Nonparametric Statistics Pages: 105-114 Issue: 1 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903194003 File-URL: http://hdl.handle.net/10.1080/10485250903194003 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:1:p:105-114 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: List of Reviewers for 2009 Journal: Pages: 131-132 Issue: 1 Volume: 22 Year: 2010 X-DOI: 10.1080/10485250903438657 File-URL: http://hdl.handle.net/10.1080/10485250903438657 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:22:y:2010:i:1:p:131-132 Template-Type: ReDIF-Article 1.0 Author-Name: Nicolas Asin Author-X-Name-First: Nicolas Author-X-Name-Last: Asin Author-Name: Jan Johannes Author-X-Name-First: Jan Author-X-Name-Last: Johannes Title: Adaptive nonparametric estimation in the presence of dependence Abstract: We consider nonparametric estimation problems in the presence of dependent data, notably nonparametric regression with random design and nonparametric density estimation. The proposed estimation procedure is based on a dimension reduction. The minimax optimal rate of convergence of the estimator is derived assuming a sufficiently weak dependence characterised by fast decreasing mixing coefficients. We illustrate these results by considering classical smoothness assumptions. However, the proposed estimator requires an optimal choice of a dimension parameter depending on certain characteristics of the function of interest, which are not known in practice. The main issue addressed in our work is an adaptive choice of this dimension parameter combining model selection and Lepski's method. It is inspired by the recent work of Goldenshluger and Lepski [(2011), ‘Bandwidth Selection in Kernel Density Estimation: Oracle Inequalities and Adaptive Minimax Optimality’, The Annals of Statistics, 39, 1608–1632]. We show that this data-driven estimator can attain the lower risk bound up to a constant provided a fast decay of the mixing coefficients. Journal: Journal of Nonparametric Statistics Pages: 694-730 Issue: 4 Volume: 29 Year: 2017 Month: 10 X-DOI: 10.1080/10485252.2017.1367788 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1367788 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:4:p:694-730 Template-Type: ReDIF-Article 1.0 Author-Name: Nikolai Dokuchaev Author-X-Name-First: Nikolai Author-X-Name-Last: Dokuchaev Title: A pathwise inference method for the parameters of diffusion terms Abstract: We consider inference of the parameters of the diffusion term for continuous time stochastic processes with a power-type dependence of the diffusion coefficient from the underlying process such as Cox–Ingersoll–Ross, CKLS, and similar processes. We suggest some original pathwise estimates for this coefficient and for the power index based on an analysis of an auxiliary continuous time complex-valued process generated by the underlying real-valued process. These estimates do not rely on the distribution of the underlying process and on a particular choice of the drift. Some numerical experiments are used to illustrate the feasibility of the suggested method. Journal: Journal of Nonparametric Statistics Pages: 731-743 Issue: 4 Volume: 29 Year: 2017 Month: 10 X-DOI: 10.1080/10485252.2017.1367789 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1367789 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:4:p:731-743 Template-Type: ReDIF-Article 1.0 Author-Name: Graciela Boente Author-X-Name-First: Graciela Author-X-Name-Last: Boente Author-Name: Alejandra Martínez Author-X-Name-First: Alejandra Author-X-Name-Last: Martínez Author-Name: Matías Salibián-Barrera Author-X-Name-First: Matías Author-X-Name-Last: Salibián-Barrera Title: Robust estimators for additive models using backfitting Abstract: Additive models provide an attractive setup to estimate regression functions in a nonparametric context. They provide a flexible and interpretable model, where each regression function depends only on a single explanatory variable and can be estimated at an optimal univariate rate. Most estimation procedures for these models are highly sensitive to the presence of even a small proportion of outliers in the data. In this paper, we show that a relatively simple robust version of the backfitting algorithm (consisting of using robust local polynomial smoothers) corresponds to the solution of a well-defined optimisation problem. This formulation allows us to find mild conditions to show Fisher consistency and to study the convergence of the algorithm. Our numerical experiments show that the resulting estimators have good robustness and efficiency properties. We illustrate the use of these estimators on a real data set where the robust fit reveals the presence of influential outliers. Journal: Journal of Nonparametric Statistics Pages: 744-767 Issue: 4 Volume: 29 Year: 2017 Month: 10 X-DOI: 10.1080/10485252.2017.1369077 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1369077 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:4:p:744-767 Template-Type: ReDIF-Article 1.0 Author-Name: W. Rejchel Author-X-Name-First: W. Author-X-Name-Last: Rejchel Title: Model selection consistency of -statistics with convex loss and weighted lasso penalty Abstract: In the paper we consider minimisation of U-statistics with the weighted Lasso penalty and investigate their asymptotic properties in model selection and estimation. We prove that the use of appropriate weights in the penalty leads to the procedure that behaves like the oracle that knows the true model in advance, i.e. it is model selection consistent and estimates nonzero parameters with the standard rate. For the unweighted Lasso penalty, we obtain sufficient and necessary conditions for model selection consistency of estimators. The obtained results strongly based on the convexity of the loss function that is the main assumption of the paper. Our theorems can be applied to the ranking problem as well as generalised regression models. Thus, using U-statistics we can study more complex models (better describing real problems) than usually investigated linear or generalised linear models. Journal: Journal of Nonparametric Statistics Pages: 768-791 Issue: 4 Volume: 29 Year: 2017 Month: 10 X-DOI: 10.1080/10485252.2017.1369078 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1369078 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:4:p:768-791 Template-Type: ReDIF-Article 1.0 Author-Name: Asma Jmaei Author-X-Name-First: Asma Author-X-Name-Last: Jmaei Author-Name: Yousri Slaoui Author-X-Name-First: Yousri Author-X-Name-Last: Slaoui Author-Name: Wassima Dellagi Author-X-Name-First: Wassima Author-X-Name-Last: Dellagi Title: Recursive distribution estimator defined by stochastic approximation method using Bernstein polynomials Abstract: We propose a recursive distribution estimator using Robbins-Monro's algorithm and Bernstein polynomials. We study the properties of the recursive estimator, as a competitor of Vitale's distribution estimator. We show that, with optimal parameters, our proposal dominates Vitale's estimator in terms of the mean integrated squared error. Finally, we confirm theoretical result throught a simulation study. Journal: Journal of Nonparametric Statistics Pages: 792-805 Issue: 4 Volume: 29 Year: 2017 Month: 10 X-DOI: 10.1080/10485252.2017.1369538 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1369538 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:4:p:792-805 Template-Type: ReDIF-Article 1.0 Author-Name: D.P. Amali Dassanayake Author-X-Name-First: D.P. Author-X-Name-Last: Amali Dassanayake Author-Name: Igor Volobouev Author-X-Name-First: Igor Author-X-Name-Last: Volobouev Author-Name: A. Alexandre Trindade Author-X-Name-First: A. Alexandre Author-X-Name-Last: Trindade Title: Local orthogonal polynomial expansion for density estimation Abstract: A local orthogonal polynomial expansion (LOrPE) of the empirical density function is proposed as a novel method to estimate the underlying density. The estimate is constructed by matching localised expectation values of orthogonal polynomials to the values observed in the sample. LOrPE is related to several existing methods, and generalises straightforwardly to multivariate settings. By manner of construction, it is similar to local likelihood density estimation (LLDE). In the limit of small bandwidths, LOrPE functions as kernel density estimation (KDE) with high-order (effective) kernels inherently free of boundary bias, a natural consequence of kernel reshaping to accommodate endpoints. Consistency and faster asymptotic convergence rates follow. In the limit of large bandwidths LOrPE is equivalent to orthogonal series density estimation (OSDE) with Legendre polynomials, thereby inheriting its consistency. We compare the performance of LOrPE to KDE, LLDE, and OSDE, in a number of simulation studies. In terms of mean integrated squared error, the results suggest that with a proper balance of the two tuning parameters, bandwidth and degree, LOrPE generally outperforms these competitors when estimating densities with sharply truncated supports. Journal: Journal of Nonparametric Statistics Pages: 806-830 Issue: 4 Volume: 29 Year: 2017 Month: 10 X-DOI: 10.1080/10485252.2017.1371715 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1371715 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:4:p:806-830 Template-Type: ReDIF-Article 1.0 Author-Name: Zhong Guan Author-X-Name-First: Zhong Author-X-Name-Last: Guan Title: Bernstein polynomial model for grouped continuous data Abstract: Grouped data are commonly encountered in applications. All data from a continuous population are grouped due to rounding of the individual observations. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein polynomial, as the mixture proportions of beta distributions, can be estimated using an EM algorithm. The optimal degree of the Bernstein polynomial can be determined using a change-point estimation method. The rate of convergence of the proposed density estimate to the true density is proved to be almost parametric by an acceptance–rejection argument used for generating random numbers. The proposed method is compared with some existing methods in a simulation study and is applied to the Chicken Embryo Data. Journal: Journal of Nonparametric Statistics Pages: 831-848 Issue: 4 Volume: 29 Year: 2017 Month: 10 X-DOI: 10.1080/10485252.2017.1374384 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1374384 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:4:p:831-848 Template-Type: ReDIF-Article 1.0 Author-Name: Min Chen Author-X-Name-First: Min Author-X-Name-Last: Chen Author-Name: Yimin Lian Author-X-Name-First: Yimin Author-X-Name-Last: Lian Author-Name: Zhao Chen Author-X-Name-First: Zhao Author-X-Name-Last: Chen Author-Name: Zhengjun Zhang Author-X-Name-First: Zhengjun Author-X-Name-Last: Zhang Title: Sure explained variability and independence screening Abstract: In the era of Big Data, extracting the most important exploratory variables available in ultrahigh-dimensional data plays a key role in scientific researches. Existing researches have been mainly focusing on applying the extracted exploratory variables to describe the central tendency of their related response variables. For a response variable, its variability characteristic is as much important as the central tendency in statistical inference. This paper focuses on the variability and proposes a new model-free feature screening approach: sure explained variability and independence screening (SEVIS). The core of SEVIS is to take the advantage of recently proposed asymmetric and nonlinear generalised measures of correlation in the screening. Under some mild conditions, the paper shows that SEVIS not only possesses desired sure screening property and ranking consistency property, but also is a computational convenient variable selection method to deal with ultrahigh-dimensional data sets with more features than observations. The superior performance of SEVIS, compared with existing model-free methods, is illustrated in extensive simulations. A real example in ultrahigh-dimensional variable selection demonstrates that the variables selected by SEVIS better explain not only the response variables, but also the variables selected by other methods. Journal: Journal of Nonparametric Statistics Pages: 849-883 Issue: 4 Volume: 29 Year: 2017 Month: 10 X-DOI: 10.1080/10485252.2017.1375111 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1375111 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:4:p:849-883 Template-Type: ReDIF-Article 1.0 Author-Name: Guanghui Cheng Author-X-Name-First: Guanghui Author-X-Name-Last: Cheng Author-Name: Zhengjun Zhang Author-X-Name-First: Zhengjun Author-X-Name-Last: Zhang Author-Name: Baoxue Zhang Author-X-Name-First: Baoxue Author-X-Name-Last: Zhang Title: Test for bandedness of high-dimensional precision matrices Abstract: Statistical inferences in high-dimensional precision matrices are equally important as statistical inferences in high-dimensional covariance matrices. In the literature, much attention has been paid to the latter, and significant advances have been achieved, especially in estimation and test of the banded structure. This paper proposes a new test for testing banded structures of precision matrices without assuming any specific parametric distribution. The test is adapted to the large p small n problems in which we derive the asymptotic distribution under the null hypothesis of bandedness. Simulation results show that the proposed test performs well with finite sample sizes. A real data application is realised to a phone call centre data. Journal: Journal of Nonparametric Statistics Pages: 884-902 Issue: 4 Volume: 29 Year: 2017 Month: 10 X-DOI: 10.1080/10485252.2017.1375112 File-URL: http://hdl.handle.net/10.1080/10485252.2017.1375112 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:29:y:2017:i:4:p:884-902 Template-Type: ReDIF-Article 1.0 Author-Name: Hiroki Masuda Author-X-Name-First: Hiroki Author-X-Name-Last: Masuda Author-Name: Ilia Negri Author-X-Name-First: Ilia Author-X-Name-Last: Negri Author-Name: Yoichi Nishiyama Author-X-Name-First: Yoichi Author-X-Name-Last: Nishiyama Title: Goodness-of-fit test for ergodic diffusions by discrete-time observations: an innovation martingale approach Abstract: We consider a nonparametric goodness-of-fit test problem for the drift coefficient of one-dimensional ergodic diffusions. Our test is based on the discrete-time observation of the processes, and the diffusion coefficient is a nuisance function which is estimated in some sense in our testing procedure. We prove that the limit distribution of our test is the supremum of the standard Brownian motion, and thus our test is asymptotically distribution free. We also show that our test is consistent under any fixed alternatives. Journal: Journal of Nonparametric Statistics Pages: 237-254 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.510186 File-URL: http://hdl.handle.net/10.1080/10485252.2010.510186 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:237-254 Template-Type: ReDIF-Article 1.0 Author-Name: Xiaohui Liu Author-X-Name-First: Xiaohui Author-X-Name-Last: Liu Author-Name: Zhizhong Wang Author-X-Name-First: Zhizhong Author-X-Name-Last: Wang Author-Name: Xuemei Hu Author-X-Name-First: Xuemei Author-X-Name-Last: Hu Title: Testing heteroscedasticity in partially linear models with missing covariates Abstract: The purpose of this paper is to investigate the underlying heteroscedasticity in a partially linear model with missing covariates by using the empirical likelihood method. Two new test statistics are proposed based on the inverse probability-weighted idea. Under the null hypothesis, the resulting test statistics are shown to have standard chi-squared distributions asymptotically. Simulation studies show that the proposed statistics behave well. An example of an AIDS clinical trial data set is also used for illustrating our methods. Journal: Journal of Nonparametric Statistics Pages: 321-337 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.515306 File-URL: http://hdl.handle.net/10.1080/10485252.2010.515306 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:321-337 Template-Type: ReDIF-Article 1.0 Author-Name: Auguste Gaddah Author-X-Name-First: Auguste Author-X-Name-Last: Gaddah Author-Name: Roel Braekers Author-X-Name-First: Roel Author-X-Name-Last: Braekers Title: An extension of the Koziol–Green model under dependent censoring Abstract: In survival analysis, the classical Koziol–Green model under random censorship is commonly used for informative censoring. We propose in this paper an extension of this model in which we derive a nonparametric estimator for the distribution function of a survival time under two types of informative censoring. For the first type of informative censoring, we assume that the censoring time depends on the survival time through the expression of their joint distribution by an Archimedean copula. For the second type of informative censoring, we assume that the marginal distribution of the censoring time is a function of the marginal distribution of the survival time where this function is found through a section of a known copula function on the observed lifetime and the censoring indicator. We prove in this paper the uniform consistency of the new estimator and show the weak convergence of the associated process. Afterwards, we give some finite sample simulation results and illustrate this estimator on a real-life data set. Journal: Journal of Nonparametric Statistics Pages: 439-453 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.515682 File-URL: http://hdl.handle.net/10.1080/10485252.2010.515682 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:439-453 Template-Type: ReDIF-Article 1.0 Author-Name: Zhensheng Huang Author-X-Name-First: Zhensheng Author-X-Name-Last: Huang Title: Statistical estimation in partially linear single-index models with error-prone linear covariates Abstract: This article considers a class of partially linear single-index models when some linear covariates are not observed, but their ancillary variables are available. This model can avoid the ‘curse of dimensionality’ in multivariate nonparametric regressions, and it contains many existing statistical models such as the partially linear model (Engle, R.F., Granger, W. J., Rice, J., and Weiss, A. (1986), ‘Semiparametric Estimates of the Relation Between Weather and Electricity Sales’, Journal of The American Statistical Association, 80, 310–319), the single-index model (Härdle, W., Hall, P., and Ichimura, H. (1993), ‘Optimal Smoothing in Single-Index Models’, The Annals of Statistics, 21, 157–178), the partially linear errors-in-variables model (Liang, H., Härdle, W., and Carroll, R.J. (1999), ‘Estimation in a Semi-parametric Partially Linear Errors-in-Variables Model’, The Annals of Statistics, 27, 1519–1535), the partially linear single-index measurement error model (Liang, H., and Wang, N. (2005), ‘Partially Linear Single-Index Measurement Error Models’, Statistica Sinica, 15, 99–116), and so on as special examples. In this article, an estimation procedure for the unknowns of the proposed models is proposed, and asymptotic properties of the corresponding estimators are derived. Finite sample performance of the proposed methodology is assessed by Monte Carlo simulation studies. A real example is also given to illustrate the proposed procedures. Journal: Journal of Nonparametric Statistics Pages: 339-350 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.518705 File-URL: http://hdl.handle.net/10.1080/10485252.2010.518705 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:339-350 Template-Type: ReDIF-Article 1.0 Author-Name: Rong Chen Author-X-Name-First: Rong Author-X-Name-Last: Chen Author-Name: Hua Liang Author-X-Name-First: Hua Author-X-Name-Last: Liang Author-Name: Jing Wang Author-X-Name-First: Jing Author-X-Name-Last: Wang Title: Determination of linear components in additive models Abstract: Additive models have been widely used in nonparametric regression, mainly due to their ability to avoid the problem of the ‘curse of dimensionality’. When some of the additive components are linear, the model can be further simplified and higher convergence rates can be achieved for the estimation of these linear components. In this paper, we propose a testing procedure for the determination of linear components in nonparametric additive models. We adopt the penalised spline approach for modelling the nonparametric functions, and the test is a sort of Chi-square test based on finite-order penalised spline estimators. The limiting behaviour of the test statistic is investigated. To obtain the critical values for finite sample problems, we use resampling techniques to establish a bootstrap test. The performance of the proposed tests is studied through simulation experiments and a real-data example. Journal: Journal of Nonparametric Statistics Pages: 367-383 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.520713 File-URL: http://hdl.handle.net/10.1080/10485252.2010.520713 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:367-383 Template-Type: ReDIF-Article 1.0 Author-Name: Marc Hallin Author-X-Name-First: Marc Author-X-Name-Last: Hallin Author-Name: Yvik Swan Author-X-Name-First: Yvik Author-X-Name-Last: Swan Author-Name: Thomas Verdebout Author-X-Name-First: Thomas Author-X-Name-Last: Verdebout Author-Name: David Veredas Author-X-Name-First: David Author-X-Name-Last: Veredas Title: Rank-based testing in linear models with stable errors Abstract: Linear models with stable error densities are considered, and their local asymptotic normality with respect to the regression parameter is established. We use this result, combined with Le Cam's third lemma, to obtain local powers and asymptotic relative efficiencies for various classical rank tests (the regression and analysis of variance counterparts of the Wilcoxon, van der Waerden and median tests) under α-stable densities with various values of the skewness parameter and tail index. The same results are used to construct new rank tests, based on ‘stable scores’, achieving parametric optimality at specified stable densities. A Monte Carlo study is conducted to compare their finite-sample relative performances. Journal: Journal of Nonparametric Statistics Pages: 305-320 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.525234 File-URL: http://hdl.handle.net/10.1080/10485252.2010.525234 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:305-320 Template-Type: ReDIF-Article 1.0 Author-Name: Vesa Hasu Author-X-Name-First: Vesa Author-X-Name-Last: Hasu Author-Name: Kalle Halmevaara Author-X-Name-First: Kalle Author-X-Name-Last: Halmevaara Author-Name: Heikki Koivo Author-X-Name-First: Heikki Author-X-Name-Last: Koivo Title: An approximation procedure of quantiles using an estimation of kernel method for quality control Abstract: Testing measurements against quantiles of their distributions is a basic quality control technique. Unfortunately, the methods for the empirical quantile computation require usually ordered observations, which is not feasible for on-line use in large systems. This paper proposes a procedure for approximation of quantiles from a random sample of observations. The procedure is applicable on-line without exhaustive database searches, and it enables also approximation of high quantiles and nonstationary distributions. Our approach is based on using a linear approximation of the kernel smoothed quantile estimation for the cumulative distribution function. We apply the procedure in the quality control of temperature measurement with a tail frequency estimation approach. Journal: Journal of Nonparametric Statistics Pages: 399-413 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.526210 File-URL: http://hdl.handle.net/10.1080/10485252.2010.526210 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:399-413 Template-Type: ReDIF-Article 1.0 Author-Name: Mary Meyer Author-X-Name-First: Mary Author-X-Name-Last: Meyer Author-Name: Desale Habtzghi Author-X-Name-First: Desale Author-X-Name-Last: Habtzghi Title: Nonparametric estimation of density and hazard rate functions with shape restrictions Abstract: Methods for nonparametric maximum likelihood estimation of probability distributions are presented, with assumptions concerning the smoothness and shape. In particular, the decreasing density is considered, as well as constraints on the hazard function including increasing, convex or bathtub-shaped, and increasing and convex. Regression splines are used to formulate the problem in terms of convex programming, and iteratively re-weighted least squares cone projection algorithms are proposed. The estimators obtain the convergence rate r=(p+1)/(2p+3) where p is the degree of the polynomial spline. The method can be used with right-censored data. These methods are applied to real and simulated data sets to illustrate the small sample properties of the estimators and to compare with existing nonparametric estimators. Journal: Journal of Nonparametric Statistics Pages: 455-470 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.531133 File-URL: http://hdl.handle.net/10.1080/10485252.2010.531133 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:455-470 Template-Type: ReDIF-Article 1.0 Author-Name: Yongsong Qin Author-X-Name-First: Yongsong Author-X-Name-Last: Qin Author-Name: Jianjun Li Author-X-Name-First: Jianjun Author-X-Name-Last: Li Title: Empirical likelihood for partially linear models with missing responses at random Abstract: Suppose that we have a partially linear model Yi=X′iβ+g(Ti)+εi with E(ε|X, T)=0, where {Xi, Ti, i=1, …, n} are random and observed completely, and {Yi, i=1, …, n} are missing at random (MAR). Empirical likelihood (EL) ratio statistics for the regression coefficient β and the nonparametric function g(t0) for fixed t0∈(0, 1) are constructed based on the inverse probability weighted imputation approach, which asymptotically have χ2-type distributions. These results are used to obtain EL-based confidence regions for β and g(t0). Results of a simulation study on the finite sample performance of EL-based confidence regions are presented. Journal: Journal of Nonparametric Statistics Pages: 497-511 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.531134 File-URL: http://hdl.handle.net/10.1080/10485252.2010.531134 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:497-511 Template-Type: ReDIF-Article 1.0 Author-Name: Ani Eloyan Author-X-Name-First: Ani Author-X-Name-Last: Eloyan Author-Name: Sujit Ghosh Author-X-Name-First: Sujit Author-X-Name-Last: Ghosh Title: Smooth density estimation with moment constraints using mixture distributions Abstract: Statistical analysis often involves the estimation of a probability density based on a sample of observations. A commonly used nonparametric method for solving this problem is the kernel-based method. The motivation is that any continuous density can be approximated by a mixture of densities with appropriately chosen bandwidths. In many practical applications, we may have specific information about the moments of the density. A nonparametric method using a mixture of known densities is proposed that conserves a given set of moments. A modified expectation–maximisation algorithm for estimating the weights of the mixture density is then developed. The proposed method also obtains an estimate of the number of components in the mixture needed for optimal approximation. The proposed method is compared with two popular density estimation methods using simulated data and it is shown that the proposed estimate outperforms the others. The method is then illustrated by applying it to several real-data examples. Journal: Journal of Nonparametric Statistics Pages: 513-531 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.532554 File-URL: http://hdl.handle.net/10.1080/10485252.2010.532554 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:513-531 Template-Type: ReDIF-Article 1.0 Author-Name: Amal Helu Author-X-Name-First: Amal Author-X-Name-Last: Helu Author-Name: Hani Samawi Author-X-Name-First: Hani Author-X-Name-Last: Samawi Author-Name: Robert Vogel Author-X-Name-First: Robert Author-X-Name-Last: Vogel Title: Nonparametric overlap coefficient estimation using ranked set sampling Abstract: Ranked set sampling is used to produce a nonparametric kernel estimator of the overlap measure. Some asymptotic properties of the kernel estimator of overlap measure are established. Simulation studies are used to get an insight about the performance of the estimator when the ranked set sampling is used. Illustration using real data is also provided. Journal: Journal of Nonparametric Statistics Pages: 385-397 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.533769 File-URL: http://hdl.handle.net/10.1080/10485252.2010.533769 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:385-397 Template-Type: ReDIF-Article 1.0 Author-Name: Yufeng Liu Author-X-Name-First: Yufeng Author-X-Name-Last: Liu Author-Name: Yichao Wu Author-X-Name-First: Yichao Author-X-Name-Last: Wu Title: Simultaneous multiple non-crossing quantile regression estimation using kernel constraints Abstract: Quantile regression (QR) is a very useful statistical tool for learning the relationship between the response variable and covariates. For many applications, one often needs to estimate multiple conditional quantile functions of the response variable given covariates. Although one can estimate multiple quantiles separately, it is of great interest to estimate them simultaneously. One advantage of simultaneous estimation is that multiple quantiles can share strength among them to gain better estimation accuracy than individually estimated quantile functions. Another important advantage of joint estimation is the feasibility of incorporating simultaneous non-crossing constraints of QR functions. In this paper, we propose a new kernel-based multiple QR estimation technique, namely simultaneous non-crossing quantile regression (SNQR). We use kernel representations for QR functions and apply constraints on the kernel coefficients to avoid crossing. Both unregularised and regularised SNQR techniques are considered. Asymptotic properties such as asymptotic normality of linear SNQR and oracle properties of the sparse linear SNQR are developed. Our numerical results demonstrate the competitive performance of our SNQR over the original individual QR estimation. Journal: Journal of Nonparametric Statistics Pages: 415-437 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.537336 File-URL: http://hdl.handle.net/10.1080/10485252.2010.537336 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:415-437 Template-Type: ReDIF-Article 1.0 Author-Name: Carlos Tenreiro Author-X-Name-First: Carlos Author-X-Name-Last: Tenreiro Title: Fourier series-based direct plug-in bandwidth selectors for kernel density estimation Abstract: A class of Fourier series-based direct plug-in bandwidth selectors for kernel density estimation is considered in this paper. The proposed bandwidth estimators have a relative convergence rate n−1/2 whenever the underlying density is smooth enough and the simulation results testify that they present a very good finite sample performance against the most recommended bandwidth selection methods in the literature. Journal: Journal of Nonparametric Statistics Pages: 533-545 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.537337 File-URL: http://hdl.handle.net/10.1080/10485252.2010.537337 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:533-545 Template-Type: ReDIF-Article 1.0 Author-Name: J. Franke Author-X-Name-First: J. Author-X-Name-Last: Franke Author-Name: J.-P. Stockis Author-X-Name-First: J.-P. Author-X-Name-Last: Stockis Author-Name: J. Tadjuidje-Kamgaing Author-X-Name-First: J. Author-X-Name-Last: Tadjuidje-Kamgaing Author-Name: W. Li Author-X-Name-First: W. Author-X-Name-Last: Li Title: Mixtures of nonparametric autoregressions Abstract: We consider data generating mechanisms which can be represented as mixtures of finitely many regression or autoregression models. We propose nonparametric estimators for the functions characterising the various mixture components based on a local quasi maximum likelihood approach and prove their consistency. We present an EM algorithm for calculating the estimates numerically which is mainly based on iteratively applying common local smoothers and discuss its convergence properties. Journal: Journal of Nonparametric Statistics Pages: 287-303 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.539686 File-URL: http://hdl.handle.net/10.1080/10485252.2010.539686 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:287-303 Template-Type: ReDIF-Article 1.0 Author-Name: Melanie Birke Author-X-Name-First: Melanie Author-X-Name-Last: Birke Author-Name: Holger Dette Author-X-Name-First: Holger Author-X-Name-Last: Dette Author-Name: Kristin Stahljans Author-X-Name-First: Kristin Author-X-Name-Last: Stahljans Title: Testing symmetry of a nonparametric bivariate regression function Abstract: We propose a test for symmetry of a regression function with a bivariate predictor based on the L2 distance between the original function and its reflection. This distance is estimated by kernel methods and it is shown that under the null hypothesis as well as under the alternative the test statistic is asymptotically normally distributed. The finite sample properties of a bootstrap version of this test are investigated by means of a simulation study and a possible application in detecting asymmetries in grey-scale images is discussed. Journal: Journal of Nonparametric Statistics Pages: 547-565 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.539687 File-URL: http://hdl.handle.net/10.1080/10485252.2010.539687 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:547-565 Template-Type: ReDIF-Article 1.0 Author-Name: L. Galtchouk Author-X-Name-First: L. Author-X-Name-Last: Galtchouk Author-Name: S. Pergamenshchikov Author-X-Name-First: S. Author-X-Name-Last: Pergamenshchikov Title: Adaptive sequential estimation for ergodic diffusion processes in quadratic metric Abstract: An adaptive nonparametric procedure is constructed for estimating the unknown drift coefficient in ergodic diffusion processes. A sharp non-asymptotic upper bound (an oracle inequality) is obtained for a quadratic risk. Furthermore, an asymptotic lower bound for the minimax quadratic risk is found that equals to the Pinsker constant. Asymptotic efficiency is proved, that is, the asymptotic quadratic risk of the constructed estimator coincides with this constant. Journal: Journal of Nonparametric Statistics Pages: 255-285 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.544307 File-URL: http://hdl.handle.net/10.1080/10485252.2010.544307 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:255-285 Template-Type: ReDIF-Article 1.0 Author-Name: Elodie Brunel Author-X-Name-First: Elodie Author-X-Name-Last: Brunel Author-Name: Fabienne Comte Author-X-Name-First: Fabienne Author-X-Name-Last: Comte Title: Conditional mean residual life estimation Abstract: In this paper, we consider the problem of nonparametric mean residual life (MRL) function estimation in presence of covariates. We propose a contrast that provides estimators of the bivariate conditional MRL function, when minimised over different collections of linear finite-dimensional function spaces. Then we describe a model selection device to select the best estimator among the collection, in the mean integrated squared error sense. A non-asymptotic oracle inequality is proved for the estimator, which both ensures the good finite sample performances of the estimator and allows us to compute asymptotic rates of convergence. Lastly, examples and simulation experiments illustrate the method, together with a short real data study. Journal: Journal of Nonparametric Statistics Pages: 471-495 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.544731 File-URL: http://hdl.handle.net/10.1080/10485252.2010.544731 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:471-495 Template-Type: ReDIF-Article 1.0 Author-Name: Gang Cheng Author-X-Name-First: Gang Author-X-Name-Last: Cheng Author-Name: Ying Zhang Author-X-Name-First: Ying Author-X-Name-Last: Zhang Author-Name: Liqiang Lu Author-X-Name-First: Liqiang Author-X-Name-Last: Lu Title: Efficient algorithms for computing the non and semi-parametric maximum likelihood estimates with panel count data Abstract: Nonparametric and semi-parametric analysis of panel count data have recently been active research topics in statistical literature. The maximum likelihood method based on the non-homogeneous Poisson process has been proved an efficient inference procedure for such analysis. However, computing the non- and semi-parametric maximum likelihood estimates (MLEs) can be very intensive numerically and the available methods are not efficient. In this manuscript, we develop an efficient numerical algorithm stemming from the Newton–Raphson method to compute the non- and semi-parametric MLEs for panel count data. Simulation studies are carried out to demonstrate the numerical efficiency of the proposed algorithm compared to the existing methods in the literature. Journal: Journal of Nonparametric Statistics Pages: 567-579 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2010.548521 File-URL: http://hdl.handle.net/10.1080/10485252.2010.548521 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:567-579 Template-Type: ReDIF-Article 1.0 Author-Name: Han-Ying Liang Author-X-Name-First: Han-Ying Author-X-Name-Last: Liang Author-Name: Ya-Mei Liu Author-X-Name-First: Ya-Mei Author-X-Name-Last: Liu Title: Asymptotic normality of variance estimator in a heteroscedastic model with dependent errors Abstract: Consider the heteroscedastic regression model Yni=g(xni)+σniεni (1≤i≤n), where , the design points (xni, uni) are known and nonrandom, g(·) and f(·) are unknown functions defined on [0, 1], and the random errors {εni, 1≤i≤n} are assumed to have the same distribution as {ξi, 1≤i≤n}, which is a stationary and α-mixing time series with Eξi=0. Under appropriate conditions, we study the asymptotic normality of an estimator of the function f(·). At the same time, we derive a Berry–Esseen-type bound for the estimator. As a corollary, by making a certain choice of the weights, the Berry–Esseen-type bound of the estimator can attain O(n−1/12(log n)−1/3). Finite sample behaviour of this estimator is investigated too. Journal: Journal of Nonparametric Statistics Pages: 351-365 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.552721 File-URL: http://hdl.handle.net/10.1080/10485252.2011.552721 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:351-365 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Student Prize Award Abstract: P-splines regression is a flexible smoothing tool in which the starting point is a highly parameterised model and overfitting is prevented by introducing a penalty function. A common form of the penalty term is obtained by taking a prespecified order of differences of adjacent coefficients. This paper deals with a data-driven choice of the differencing order, as such allowing for the fit to adapt automatically to the (unknown) degree of smoothness of the underlying function. The selection procedure is based on Akaike's information criterion. The study is carried out in a broad framework of generalised linear and generalised additive models. We provide the necessary theoretical support for the selection procedure, and investigate its performance via simulations. We illustrate the use of such a selection procedure on some real data examples. The discussed examples include generalised normal, binomial and Poisson regression models. Journal: Pages: 581-581 Issue: 2 Volume: 23 Year: 2011 X-DOI: 10.1080/10485252.2011.573627 File-URL: http://hdl.handle.net/10.1080/10485252.2011.573627 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:581-581 Template-Type: ReDIF-Article 1.0 Author-Name: Lee-Shen Chen Author-X-Name-First: Lee-Shen Author-X-Name-Last: Chen Title: On empirical Bayes two-tail tests for double exponential distributions Abstract: This paper deals with the problem of testing the hypotheses H0: |θ−θ0|≤c against H1: |θ−θ0|>c for the location parameter θ of a double exponential distribution with the probability density f(x|θ)=exp(−|x−θ|)/2 by using the empirical Bayes approach. We construct an empirical Bayes test δ*n and study its associated asymptotic optimality. Three classes of prior distributions are considered. For priors in each class, the associated rates of convergence of δ*n are established. These rates are O(n−2m/(2m+3)), O((ln n)3/s/n), and O(n−1), respectively, where m>1 and s≥1 are determined according to some conditions. Journal: Journal of Nonparametric Statistics Pages: 1037-1049 Issue: 8 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902971724 File-URL: http://hdl.handle.net/10.1080/10485250902971724 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:8:p:1037-1049 Template-Type: ReDIF-Article 1.0 Author-Name: Christophe Ley Author-X-Name-First: Christophe Author-X-Name-Last: Ley Author-Name: Davy Paindaveine Author-X-Name-First: Davy Author-X-Name-Last: Paindaveine Title: Le Cam optimal tests for symmetry against Ferreira and Steel's general skewed distributions Abstract: When testing symmetry of a univariate density, (parametric classes of) densities skewed by means of the general probability transform introduced in Ferreira and Steel [A constructive representation of univariate skewed distributions, J. Amer. Statist. Assoc. 101 (2006), pp. 823–829] are appealing alternatives. This paper first proposes parametric tests of symmetry (about a specified centre) that are locally and asymptotically optimal (in the Le Cam sense) against such alternatives. To improve on these parametric tests, which are valid under well-specified density types only, we turn them into semiparametric tests, either by using a standard studentisation approach or by resorting to the invariance principle. The second approach leads to robust yet efficient signed-rank tests, which include the celebrated sign and Wilcoxon tests as special cases, and turn out to be Le Cam optimal irrespective of the underlying original symmetric density. Optimality, however, is only achieved under well-specified ‘skewing mechanisms’, and we therefore evaluate the overall performances of our tests by deriving their asymptotic relative efficiencies with respect to the classical test of skewness. A Monte-Carlo study confirms the asymptotic results. Journal: Journal of Nonparametric Statistics Pages: 943-967 Issue: 8 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902971765 File-URL: http://hdl.handle.net/10.1080/10485250902971765 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:8:p:943-967 Template-Type: ReDIF-Article 1.0 Author-Name: J. Chacón Author-X-Name-First: J. Author-X-Name-Last: Chacón Author-Name: J. Montanero Author-X-Name-First: J. Author-X-Name-Last: Montanero Author-Name: A. Nogales Author-X-Name-First: A. Author-X-Name-Last: Nogales Author-Name: P. Pérez Author-X-Name-First: P. Author-X-Name-Last: Pérez Title: Partial sufficiency and density estimation Abstract: In this paper, we study the usefulness of the concept of partial sufficiency, in the sense of Fraser, when it is applied to the problem of nonparametric density estimation. Journal: Journal of Nonparametric Statistics Pages: 969-975 Issue: 8 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902980550 File-URL: http://hdl.handle.net/10.1080/10485250902980550 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:8:p:969-975 Template-Type: ReDIF-Article 1.0 Author-Name: J.-Y. Brua Author-X-Name-First: J.-Y. Author-X-Name-Last: Brua Title: Adaptive estimators for nonparametric heteroscedastic regression models Abstract: This paper deals with the estimation of a regression function at a fixed point in nonparametric heteroscedastic regression models with Gaussian noise. We assume that the variance of the noise depends on the regressor and on the regression function. We make use of the minimax absolute error risk taken over a Hölder class of regression functions. As the smoothness of the regression function is supposed to be unknown, we construct an adaptive kernel estimator which attains the minimax rate. More precisely, we give an asymptotic upper bound and an asymptotic lower bound for the minimax risk. Journal: Journal of Nonparametric Statistics Pages: 991-1002 Issue: 8 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250902993645 File-URL: http://hdl.handle.net/10.1080/10485250902993645 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:8:p:991-1002 Template-Type: ReDIF-Article 1.0 Author-Name: Enrico Ciavolino Author-X-Name-First: Enrico Author-X-Name-Last: Ciavolino Author-Name: Amjad Al-Nasser Author-X-Name-First: Amjad Author-X-Name-Last: Al-Nasser Title: Comparing generalised maximum entropy and partial least squares methods for structural equation models Abstract: The generalised maximum entropy (GME) method is presented for estimating structural equation models, where a real data set of the Service & Motor Vehicle Industry in Sweden is used to show the implementation of the method. Monte Carlo simulation comparisons are also made between GME and partial least squares (PLS) methods in the presence of messy data. Three cases are considered: outliers, missing data and multicollinearity. It is shown that this method can be considered a valid alternative to the conventional method of PLS, where the results of GME, in terms of mean squared error, outperform the PLS results in some respects. Journal: Journal of Nonparametric Statistics Pages: 1017-1036 Issue: 8 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250903009037 File-URL: http://hdl.handle.net/10.1080/10485250903009037 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:8:p:1017-1036 Template-Type: ReDIF-Article 1.0 Author-Name: D. Ioannides Author-X-Name-First: D. Author-X-Name-Last: Ioannides Author-Name: Eric Matzner-Løber Author-X-Name-First: Eric Author-X-Name-Last: Matzner-Løber Title: Regression quantiles with errors-in-variables Abstract: In a lot of situations, variables are measured with errors. While this problem has been previously studied in the context of kernel regression, no work has been done in quantile regression. To estimate this function, we use deconvolution kernel estimators. We obtain asymptotic results (MSE and normality) for two estimators of conditional quantiles and analyse their finite sample performances via a large simulation study. Journal: Journal of Nonparametric Statistics Pages: 1003-1015 Issue: 8 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250903019515 File-URL: http://hdl.handle.net/10.1080/10485250903019515 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:8:p:1003-1015 Template-Type: ReDIF-Article 1.0 Author-Name: David Wozabal Author-X-Name-First: David Author-X-Name-Last: Wozabal Author-Name: Nancy Wozabal Author-X-Name-First: Nancy Author-X-Name-Last: Wozabal Title: Asymptotic consistency of risk functionals Abstract: Risk measures are functionals on spaces of random variables designed to quantify financial risk. In this paper, we consider the statistical properties of plug-in estimates for the broad class of coherent, law invariant risk functionals. In particular, we provide several sets of sufficient conditions to establish asymptotic consistency based on a general representation result for this class of functionals. We demonstrate the applicability of our approach by applying it to several well-known examples of risk functionals. Journal: Journal of Nonparametric Statistics Pages: 977-990 Issue: 8 Volume: 21 Year: 2009 X-DOI: 10.1080/10485250903060592 File-URL: http://hdl.handle.net/10.1080/10485250903060592 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:21:y:2009:i:8:p:977-990 Template-Type: ReDIF-Article 1.0 Author-Name: Shuwei Li Author-X-Name-First: Shuwei Author-X-Name-Last: Li Author-Name: Tao Hu Author-X-Name-First: Tao Author-X-Name-Last: Hu Author-Name: Jianguo Sun Author-X-Name-First: Jianguo Author-X-Name-Last: Sun Title: Regression analysis of misclassified current status data Abstract: Misclassified current status data occur when each subject under study is observed only once and the failure status at the observation time is determined by a diagnostic test with imperfect sensitivity and specificity. In this article, we provide a methodology for the analysis of such data under a wide class of flexible semiparametric transformation models. For inference, a nonparametric maximum likelihood estimation procedure is proposed along with the development of an EM algorithm. Furthermore, we show that the resulting estimators of regression parameters are consistent, asymptotically normal and semiparametrically efficient. A simulation study and a real data application demonstrate that the proposed approach performs well in practice and has substantial superiority over the naive method that ignores the misclassification. Journal: Journal of Nonparametric Statistics Pages: 1-19 Issue: 1 Volume: 32 Year: 2020 Month: 1 X-DOI: 10.1080/10485252.2019.1687892 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1687892 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:1:p:1-19 Template-Type: ReDIF-Article 1.0 Author-Name: João Lita da Silva Author-X-Name-First: João Author-X-Name-Last: Lita da Silva Title: Strong laws of large numbers for arrays of row-wise extended negatively dependent random variables with applications Abstract: The main purpose of this paper is to obtain strong laws of large numbers for arrays or weighted sums of random variables under a scenario of dependence. Namely, for triangular arrays $\{X_{n,j},\ 1 \leqslant j \leqslant n,\ n \geqslant 1\} ${Xn,j, 1⩽j⩽n, n⩾1} of row-wise extended negatively dependent random variables weakly mean dominated by a random variable $X \in \mathscr {L}_{1} $X∈L1 and sequences $\{b_{n}\} ${bn} of positive constants, conditions are given to ensure $\sum _{j=1}^{n} \left (X_{n,j} - \mathbb {E}\, X_{n,j} \right )/b_{n} \overset {\hbox{a.s.}}{\longrightarrow } 0 $∑j=1nXn,j−EXn,j/bn⟶a.s.0. Our statements allow us to establish strong consistency of general nonparametric estimates in a nonparametric regression model having fixed design points. Journal: Journal of Nonparametric Statistics Pages: 20-41 Issue: 1 Volume: 32 Year: 2020 Month: 1 X-DOI: 10.1080/10485252.2019.1688326 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1688326 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:1:p:20-41 Template-Type: ReDIF-Article 1.0 Author-Name: Christophe Denis Author-X-Name-First: Christophe Author-X-Name-Last: Denis Author-Name: Mohamed Hebiri Author-X-Name-First: Mohamed Author-X-Name-Last: Hebiri Title: Consistency of plug-in confidence sets for classification in semi-supervised learning Abstract: Confident prediction is highly relevant in machine learning; for example, in applications such as medical diagnoses, wrong prediction can be fatal. For classification, there already exist procedures that allow to not classify data when the confidence in their prediction is weak. This approach is known as classification with reject option. In this paper, we provide a new methodology for this approach. Predicting a new feature via a confidence set, we ensure an exact control of the probability of classification. Moreover, we show that this methodology can be implemented easily, in a semi-supervised way, and has attractive theoretical and numerical properties. Journal: Journal of Nonparametric Statistics Pages: 42-72 Issue: 1 Volume: 32 Year: 2020 Month: 1 X-DOI: 10.1080/10485252.2019.1689241 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1689241 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:1:p:42-72 Template-Type: ReDIF-Article 1.0 Author-Name: Yilun Sun Author-X-Name-First: Yilun Author-X-Name-Last: Sun Author-Name: Lu Wang Author-X-Name-First: Lu Author-X-Name-Last: Wang Author-Name: Peisong Han Author-X-Name-First: Peisong Author-X-Name-Last: Han Title: Multiply robust estimation in nonparametric regression with missing data Abstract: Nonparametric regression has received considerable attention in biomedical research because it allows for data-driven dependence of the response variable on covariates. In the presence of missing data, doubly robust estimators have been proposed for nonparametric regression, which allow one model for the missingness mechanism and one model for the outcome regression. We propose multiply robust kernel estimating equations (MRKEEs) for nonparametric regression that can accommodate multiple working models for either the missingness mechanism or the outcome regression, or both. The resulting estimator is consistent if any one of those models is correctly specified. When including correctly specified models for both the missingness mechanism and the outcome regression, the proposed estimator achieves the optimal efficiency within the class of augmented inverse propensity weighted (AIPW) kernel estimators. We conduct simulation studies to evaluate the finite sample performance of the proposed method and further demonstrate it through a real-data example. Journal: Journal of Nonparametric Statistics Pages: 73-92 Issue: 1 Volume: 32 Year: 2020 Month: 1 X-DOI: 10.1080/10485252.2019.1700254 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1700254 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:1:p:73-92 Template-Type: ReDIF-Article 1.0 Author-Name: Šárka Hudecová Author-X-Name-First: Šárka Author-X-Name-Last: Hudecová Author-Name: Jana Klicnarová Author-X-Name-First: Jana Author-X-Name-Last: Klicnarová Author-Name: Miroslav Šiman Author-X-Name-First: Miroslav Author-X-Name-Last: Šiman Title: Incomplete interdirections and lift-interdirections Abstract: The article presents, discusses, and explores incomplete variants of interdirections, lift-interdirections, and symmetrised lift-interdirections (with a few incomplete designs). Although they are easier to compute in high-dimensional spaces than the originals, they can still replace them in many optimal statistical procedures based on signs and ranks without significantly changing their properties. This is proved theoretically and confirmed empirically in a small simulation study dealing with the canonical examples of multivariate sign and signed-rank one-sample tests applied to high-dimensional data sets. Journal: Journal of Nonparametric Statistics Pages: 93-108 Issue: 1 Volume: 32 Year: 2020 Month: 1 X-DOI: 10.1080/10485252.2019.1700255 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1700255 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:1:p:93-108 Template-Type: ReDIF-Article 1.0 Author-Name: Feng Guo Author-X-Name-First: Feng Author-X-Name-Last: Guo Author-Name: Wei Ma Author-X-Name-First: Wei Author-X-Name-Last: Ma Author-Name: Lei Wang Author-X-Name-First: Lei Author-X-Name-Last: Wang Title: Semiparametric estimation of copula models with nonignorable missing data Abstract: This paper investigates the estimation of parametric copula models when the data have nonignorable nonresponse. We consider the propensity follows a general semiparametric model, but the distribution of the response variable and related covariates is unspecified. To solve the identifiability problem, we use an instrumental covariate, which is related to the response variable but unrelated to the propensity given the response variable and other covariates. The generalised method of moments is applied to estimate the parameters in the propensity. Based on kernel-assisted regression approach, we construct the bias-corrected semiparametric estimating equations to improve estimation efficiency. Consistency and asymptotic normality of the proposed estimators are established. The finite-sample performance of the estimators is studied through simulation, and an application to HIV-CD4 data set is also presented. Journal: Journal of Nonparametric Statistics Pages: 109-130 Issue: 1 Volume: 32 Year: 2020 Month: 1 X-DOI: 10.1080/10485252.2019.1702660 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1702660 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:1:p:109-130 Template-Type: ReDIF-Article 1.0 Author-Name: Giorgos Bakoyannis Author-X-Name-First: Giorgos Author-X-Name-Last: Bakoyannis Title: Nonparametric tests for transition probabilities in nonhomogeneous Markov processes Abstract: This paper proposes nonparametric two-sample tests for the direct comparison of the probabilities of a particular transition between states of a continuous time nonhomogeneous Markov process with a finite state space. The proposed tests are a linear nonparametric test, an $ L^2 $L2-norm-based test and a Kolmogorov–Smirnov-type test. Significance level assessment is based on rigorous procedures, which are justified through the use of modern empirical process theory. Moreover, the $ L^2 $L2-norm and the Kolmogorov–Smirnov-type tests are shown to be consistent for every fixed alternative hypothesis. The proposed tests are also extended to more complex situations such as cases with incompletely observed absorbing states and non-Markov processes. Simulation studies show that the test statistics perform well even with small sample sizes. Finally, the proposed tests are applied to data on the treatment of early breast cancer from the European Organization for Research and Treatment of Cancer (EORTC) trial 10854, under an illness-death model. Journal: Journal of Nonparametric Statistics Pages: 131-156 Issue: 1 Volume: 32 Year: 2020 Month: 1 X-DOI: 10.1080/10485252.2019.1705298 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1705298 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:1:p:131-156 Template-Type: ReDIF-Article 1.0 Author-Name: Jun Li Author-X-Name-First: Jun Author-X-Name-Last: Li Title: Asymptotic distribution-free change-point detection based on interpoint distances for high-dimensional data Abstract: Recent advances have greatly facilitated the collection of high-dimensional data in many fields. Often the dimension of the data is much larger than the sample size, the so-called high dimension, low sample size setting. One important research problem is how to develop efficient change-point detection procedures for this new setting. Thanks to their simplicity of computation, interpoint distance-based procedures provide a potential solution to this problem. However, most of the existing distance-based procedures fail to fully utilise interpoint distances, and as a result, they suffer significant loss of power. In this paper, we propose a new asymptotic distribution-free distance-based change-point detection procedure for the high dimension, low sample size setting. The proposed procedure is proven to be consistent for detecting both location and scale changes and can also provide a consistent estimator for the change-point. Our simulation study and real data analysis show that it significantly outperforms the existing methods across a variety of settings. Journal: Journal of Nonparametric Statistics Pages: 157-184 Issue: 1 Volume: 32 Year: 2020 Month: 1 X-DOI: 10.1080/10485252.2019.1710505 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1710505 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:1:p:157-184 Template-Type: ReDIF-Article 1.0 Author-Name: Huiqiong Li Author-X-Name-First: Huiqiong Author-X-Name-Last: Li Author-Name: Chenchen Ma Author-X-Name-First: Chenchen Author-X-Name-Last: Ma Author-Name: Ni Li Author-X-Name-First: Ni Author-X-Name-Last: Li Author-Name: Jianguo Sun Author-X-Name-First: Jianguo Author-X-Name-Last: Sun Title: A vine copula approach for regression analysis of bivariate current status data with informative censoring Abstract: Bivariate current status data occur in many areas and many authors have discussed their analysis and proposed many inference procedures [Jewell, N.P., van der Laan, M.J., and Lei, X. (2005), ‘Bivariate Current Status Data with Univariate Monitoring Times’, Biometrika, 92, 847–862; Wang, N., Wang, L., and McMahan, C.S. (2015), ‘Regression Analysis of Bivariate Current Status Data Under the Gammafrailty Proportional Hazards Model Using the Em Algorithm’, Computational Statistics & Data Analysis, 83, 140–150; Hu, T., Zhou, Q., and Sun, J. (2017), ‘Regression Analysis of Bivariate Current Status Data Under the Proportional Hazards Model’, The Canadian Journal of Statistics, 45, 410–424]. However, most of these methods are for the situation where the observation or censoring is non-informative and sometimes one may face informative censoring [Zhang, Z., Sun, J., and Sun, L. (2005), ‘Statistical Analysis of Current Data with Informative Observation Times’, Statistics in Medicine, 24, 1399–1407; Chen, C.M., Lu, T.F.C., Chen, M.H., and Hsu, C.M. (2012), ‘Semiparametric Transformation Models for Current Status Data with Informative Censoring’, Biometrical Journal, 19, 641–656; Ma, L., Hu, T., and Sun, J. (2015), ‘Sieve Maximum Likelihood Regression Analysis of Dependent Current Status Data’, Biometrika, 85, 649–658], where one has to deal with three correlated random variables. In this paper, a vine copula approach is developed for regression analysis of bivariate current status data in the presence of informative censoring. The proposed estimators are shown to be strongly consistent and the asymptotic normality and efficiency of the estimated regression parameter are also established. Numerical results suggest that the proposed method works well in practice. Journal: Journal of Nonparametric Statistics Pages: 185-200 Issue: 1 Volume: 32 Year: 2020 Month: 1 X-DOI: 10.1080/10485252.2019.1710506 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1710506 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:1:p:185-200 Template-Type: ReDIF-Article 1.0 Author-Name: Yiguo Sun Author-X-Name-First: Yiguo Author-X-Name-Last: Sun Title: The LLN and CLT for U-statistics under cross-sectional dependence Abstract: In this paper we establish the law of large numbers (LLN) and central limit theorem (CLT) for second-order kernel-weighted U-statistics of cross-sectionally dependent variables. To illustrate the usefulness of our theorems, we apply the new LLN and CLT to nonparametric model misspecification testing in spatial regression framework. Monte Carlo simulations are used to assess the finite sample performance of our test statistic. Journal: Journal of Nonparametric Statistics Pages: 201-224 Issue: 1 Volume: 32 Year: 2020 Month: 1 X-DOI: 10.1080/10485252.2019.1711378 File-URL: http://hdl.handle.net/10.1080/10485252.2019.1711378 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:1:p:201-224 Template-Type: ReDIF-Article 1.0 Author-Name: Lingzhe Guo Author-X-Name-First: Lingzhe Author-X-Name-Last: Guo Author-Name: Reza Modarres Author-X-Name-First: Reza Author-X-Name-Last: Modarres Title: Nonparametric tests of independence based on interpoint distances Abstract: We present novel tests for the hypothesis of independence when the number of variables is larger than the number of vector observations. We show that two multivariate normal vectors are independent if and only if their interpoint distance are independent. The proposed test statistics exploit different properties of the sample interpoint distances. A simulation study compares the new tests with three existing tests under various scenarios, including monotone and non-monotone dependence structures. Numerical results show that the new methods are effective for independence testing. Journal: Journal of Nonparametric Statistics Pages: 225-245 Issue: 1 Volume: 32 Year: 2020 Month: 1 X-DOI: 10.1080/10485252.2020.1714613 File-URL: http://hdl.handle.net/10.1080/10485252.2020.1714613 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:1:p:225-245 Template-Type: ReDIF-Article 1.0 Author-Name: Chaowen Zheng Author-X-Name-First: Chaowen Author-X-Name-Last: Zheng Author-Name: Yichao Wu Author-X-Name-First: Yichao Author-X-Name-Last: Wu Title: Tuning parameter selection for penalised empirical likelihood with a diverging number of parameters Abstract: Penalised likelihood methods have been a success in analysing high dimensional data. Tang and Leng [(2010), ‘Penalized High-Dimensional Empirical Likelihood’, Biometrika, 97(4), 905–920] extended the penalisation approach to the empirical likelihood scenario and showed that the penalised empirical likelihood estimator could identify the true predictors consistently in the linear regression models. However, this desired selection consistency property of the penalised empirical likelihood method relies heavily on the choice of the tuning parameter. In this work, we propose a tuning parameter selection procedure for penalised empirical likelihood to guarantee that this selection consistency can be achieved. Specifically, we propose a generalised information criterion (GIC) for the penalised empirical likelihood in the linear regression case. We show that the tuning parameter selected by the GIC yields the true model consistently even when the number of predictors diverges to infinity with the sample size. We demonstrate the performance of our procedure by numerical simulations and a real data analysis. Journal: Journal of Nonparametric Statistics Pages: 246-261 Issue: 1 Volume: 32 Year: 2020 Month: 1 X-DOI: 10.1080/10485252.2020.1717491 File-URL: http://hdl.handle.net/10.1080/10485252.2020.1717491 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:1:p:246-261 Template-Type: ReDIF-Article 1.0 Author-Name: Lu Wang Author-X-Name-First: Lu Author-X-Name-Last: Wang Author-Name: Lan Xue Author-X-Name-First: Lan Author-X-Name-Last: Xue Author-Name: Lijian Yang Author-X-Name-First: Lijian Author-X-Name-Last: Yang Title: Estimation of additive frontier functions with shape constraints Abstract: Production frontier is an important concept in modern economics and has been widely used to measure production efficiency. Existing nonparametric frontier models often only allow one or low-dimensional input variables due to ‘curse-of-dimensionality’. In this paper we propose a flexible additive frontier model which quantifies the effects of multiple input variables on the maximum output. In addition, we consider the estimation of the nonparametric frontier functions with shape restrictions. Economic theory often imposes shape constraints on production frontier, such as, monotonicity and concavity. A two-step constrained polynomial spline method is proposed to give smooth estimates that automatically satisfy such shape constraints. The proposed method is not only easy to compute, but also more robust to outliers. In theory, we established uniform consistency of the proposed method. We illustrate the proposed method by both simulation studies and an application to the Norwegian farm data. The numerical studies suggest that the proposed method has superior performance by incorporating shape constraints. Journal: Journal of Nonparametric Statistics Pages: 262-293 Issue: 2 Volume: 32 Year: 2020 Month: 4 X-DOI: 10.1080/10485252.2020.1721494 File-URL: http://hdl.handle.net/10.1080/10485252.2020.1721494 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:2:p:262-293 Template-Type: ReDIF-Article 1.0 Author-Name: Xiaoli Kong Author-X-Name-First: Xiaoli Author-X-Name-Last: Kong Author-Name: Solomon W. Harrar Author-X-Name-First: Solomon W. Author-X-Name-Last: Harrar Title: High-dimensional rank-based inference Abstract: Existing high-dimensional inferential methods for comparing multiple groups test hypotheses are formulated in terms of mean vectors or location parameters. These methods are applicable mainly for metric data. Furthermore, the mean-based methods assume that moments exist and the nonparametric (location-based) ones assume elliptical-contoured distributions for the populations. In this paper, a fully nonparametric (rank-based) method is proposed. The method is applicable for metric as well as non-metric data and, hence, is applicable for ordered categorical as well as skewed and heavy tailed data. To develop the theory, we prove a novel result for studying asymptotic behaviour of quadratic forms in ranks. Simulation study shows that the developed rank-based method performs comparably well with mean-based methods when the assumptions of those methods are satisfied. However, it has significantly superior power for heavy tailed distributions with the possibility of outliers. The rank method is applied to an EEG data with the objective of examining associations between alcohol use and change in brain function. Journal: Journal of Nonparametric Statistics Pages: 294-322 Issue: 2 Volume: 32 Year: 2020 Month: 4 X-DOI: 10.1080/10485252.2020.1725004 File-URL: http://hdl.handle.net/10.1080/10485252.2020.1725004 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:2:p:294-322 Template-Type: ReDIF-Article 1.0 Author-Name: Shixiao Zhang Author-X-Name-First: Shixiao Author-X-Name-Last: Zhang Author-Name: Peisong Han Author-X-Name-First: Peisong Author-X-Name-Last: Han Author-Name: Changbao Wu Author-X-Name-First: Changbao Author-X-Name-Last: Wu Title: A multiply robust Mann-Whitney test for non-randomised pretest-posttest studies with missing data Abstract: Pretest-posttest studies are a commonly used design by social scientists, medical and health researchers to examine the effect of a treatment or an intervention. We propose an empirical likelihood based Mann-Whitney test on the equality of the response distribution functions of the treatment and control arms for non-randomised pretest-posttest studies with missing responses. The proposed test is multiply robust in the sense that multiple working models can be postulated for the propensity score of treatment assignment, the missingness probability and the outcome regression, and the validity of the test only requires certain combinations of the working models to be correctly specified. Performances of the proposed test are examined through an application to the dataset from AIDS Clinical Trials Group Protocol 175 and simulation studies. Journal: Journal of Nonparametric Statistics Pages: 323-344 Issue: 2 Volume: 32 Year: 2020 Month: 4 X-DOI: 10.1080/10485252.2020.1736290 File-URL: http://hdl.handle.net/10.1080/10485252.2020.1736290 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:2:p:323-344 Template-Type: ReDIF-Article 1.0 Author-Name: Ji Eun Moon Author-X-Name-First: Ji Eun Author-X-Name-Last: Moon Author-Name: Cheolyong Park Author-X-Name-First: Cheolyong Author-X-Name-Last: Park Author-Name: Jeongcheol Ha Author-X-Name-First: Jeongcheol Author-X-Name-Last: Ha Author-Name: Sun Young Hwang Author-X-Name-First: Sun Young Author-X-Name-Last: Hwang Author-Name: Tae Yoon Kim Author-X-Name-First: Tae Yoon Author-X-Name-Last: Kim Title: Stationarity test based on density approach Abstract: It is well known that a neighbourhood problem exists between stationarity and random walk with correlated error for any finite sample size n. That is, any stationary process is approximated by random walk with correlated error for any finite n. Hence, one cannot distinguish between them easily. In this article, we propose a stationarity test based on nonparametric density that resolves the neighbourhood problem successfully. Our stationarity test also emerges as a successful long-range dependence (LRD) stationarity test. Note that there is a similar neighbourhood problem between LRD stationarity and LRD non-stationarity [Samorodnitsky, G. (2006), ‘Long Range Dependence’, Foundations and Trends in Stochastic Systems, 1, 163–257]. Journal: Journal of Nonparametric Statistics Pages: 345-366 Issue: 2 Volume: 32 Year: 2020 Month: 4 X-DOI: 10.1080/10485252.2020.1748624 File-URL: http://hdl.handle.net/10.1080/10485252.2020.1748624 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:2:p:345-366 Template-Type: ReDIF-Article 1.0 Author-Name: Mohamed Fihri Author-X-Name-First: Mohamed Author-X-Name-Last: Fihri Author-Name: Abdelhadi Akharif Author-X-Name-First: Abdelhadi Author-X-Name-Last: Akharif Author-Name: Amal Mellouk Author-X-Name-First: Amal Author-X-Name-Last: Mellouk Author-Name: Marc Hallin Author-X-Name-First: Marc Author-X-Name-Last: Hallin Title: Efficient pseudo-Gaussian and rank-based detection of random regression coefficients Abstract: Random coefficient regression models are the regression counterparts of the classical random effects models in Analysis of Variance and panel data analysis. While several heuristic methods have been proposed for the detection of such random regression coefficients, little is known on their optimality properties. Based on a nonstandard ULAN property, we are proposing locally asymptotically optimal (in the Hájek-Le Cam sense) parametric, pseudo-Gaussian, and rank-based procedures for this problem. The asymptotic relative efficiencies (with respect to the pseudo-Gaussian procedure) of rank-based tests turn out to be quite high under heavy-tailed and skewed densities, demonstrating the importance of a careful choice of scores. Simulations reveal the excellent finite-sample performances of a class of rank-based procedures based on data-driven scores. Journal: Journal of Nonparametric Statistics Pages: 367-402 Issue: 2 Volume: 32 Year: 2020 Month: 4 X-DOI: 10.1080/10485252.2020.1748625 File-URL: http://hdl.handle.net/10.1080/10485252.2020.1748625 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:2:p:367-402 Template-Type: ReDIF-Article 1.0 Author-Name: Ralph-Antoine Vital Author-X-Name-First: Ralph-Antoine Author-X-Name-Last: Vital Author-Name: Prakash Patil Author-X-Name-First: Prakash Author-X-Name-Last: Patil Title: Goodness-of-fit test for hazard rate Abstract: In Pharmacokinetic (PK) and Pharmacodynamic (PD), the hazard rate functions play a central role in modelling time-to-event data. In the context of assessing the appropriateness of a given parametric hazard model, Huh, Y., and Hutmacher, M. [(2016), ‘Application of a Hazard-based Visual Predictive Check to Evaluate Parametric Hazard Models’, Journal of Pharmacokinetics and Pharmacodynamics, 43, 57–71] showed that a hazard-based visual predictive check is as good as a visual predictive check based on the survival function. However, for the lack of objectivity of such a visual method in this paper, we propose a nonparametric goodness-of-fit test for hazard rate functions. Besides having good power properties against the fixed alternatives, the proposed nonparametric kernel-based test also can detect alternatives converging to the null at the rate of $N^{\beta },\ \beta < 1/2, $Nβ, β<1/2, where N is the sample size. Journal: Journal of Nonparametric Statistics Pages: 403-427 Issue: 2 Volume: 32 Year: 2020 Month: 4 X-DOI: 10.1080/10485252.2020.1758317 File-URL: http://hdl.handle.net/10.1080/10485252.2020.1758317 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:2:p:403-427 Template-Type: ReDIF-Article 1.0 Author-Name: Jingru Mu Author-X-Name-First: Jingru Author-X-Name-Last: Mu Author-Name: Guannan Wang Author-X-Name-First: Guannan Author-X-Name-Last: Wang Author-Name: Li Wang Author-X-Name-First: Li Author-X-Name-Last: Wang Title: Spatial autoregressive partially linear varying coefficient models Abstract: In this article, we consider a class of partially linear spatially varying coefficient autoregressive models for data distributed over complex domains. We propose approximating the varying coefficient functions via bivariate splines over triangulation to deal with the complex boundary of the spatial domain. Under some regularity conditions, the estimated constant coefficients are asymptotically normally distributed, and the estimated varying coefficients are consistent and possess the optimal convergence rate. A penalized bivariate spline estimation method with a more flexible choice of triangulation is proposed. We further develop a fast algorithm to calculate the geodesic distance. The proposed method is much more computationally efficient than the local smoothing methods, and thus capable of handling large scales of spatial data. In addition, we propose a model selection approach to identify predictors with constant and varying effects. The performance of the proposed method is evaluated by simulation examples and the Sydney real estate dataset. Journal: Journal of Nonparametric Statistics Pages: 428-451 Issue: 2 Volume: 32 Year: 2020 Month: 4 X-DOI: 10.1080/10485252.2020.1759596 File-URL: http://hdl.handle.net/10.1080/10485252.2020.1759596 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:gnstxx:v:32:y:2020:i:2:p:428-451 Template-Type: ReDIF-Article 1.0 Author-Name: Salim Bouzebda Author-X-Name-First: Salim Author-X-Name-Last: Bouzebda Author-Name: Boutheina Nemouchi Author-X-Name-First: Boutheina Author-X-Name-Last: Nemouchi Title: Uniform consistency and uniform in bandwidth consistency for nonparametric regression estimates and conditional U-statistics involving functional data Abstract: W. Stute [(1991), Annals of Probability, 19, 812–825] introduced a class of so-called conditional U-statistics, which may be viewed as a generalisation of the Nadaraya–Watson estimates of a regression function. Stute proved their strong pointwise consistency to \[ m(\mathbf{ t}):=\mathbb{E}[\varphi(Y_{1},\ldots,Y_{m})|(X_{1},\ldots,X_{m})=\mathbf{t}],\quad \mbox{for } \mathbf{t}\in \mathbb{R}^{dm}. \] m(t):=E[ϕ(Y1,…,Ym)|(X1,…,Xm)=t],for t∈Rdm. We apply the methods developed in Dony and Mason [(2008), Bernoulli, 14(4), 1108–1133] to establish uniformity in $\mathbf {t} $t and in bandwidth consistency (i.e. $h_{n} $hn, $h_{n}\in [a_{n},b_{n}] $hn∈[an,bn] where $0