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help for ^kernreg1^
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Kernel regression (Nadaraya-Watson estimator)
----------------------------------------------

        ^kernreg1^ yvar xvar [^if^ exp] [^in^ range],
                ^b^width^(^#^)^ ^k^ercode^(^#^)^ ^np^oint^(^#^)^
                [^g^en^(^mhvar gridvar^)^ ^nog^raph graph_options]


Description
------------

^kernreg1^ calculates the Nadaraya-Watson nonparametric regression. By default,
^kernreg1^ draws the graph of the estimated conditional mean over the grid
points used for calculation connected by a line without any symbol.

Attention. Read this!!
-----------------------

Differences between ^kernreg^ and ^kernreg1^:
 1. if the ^b^width^(^#^)^ is not specified, an optimal bandwith is assumed (as in kdensity),
 2. supresses the {if abs(`z')<=3} condition for the Gaussian kernel,
 3. uses mark `use' to take account of the `if' & `in' conditions

Options
--------

^b^width^(^#^)^ specifies the smoothing parameter (bandwidth or halfwidth) of
     the kernel density estimation for ^xvar^. This parameter defines the width
     of the weight function window around each grid point.
     If no ^b^width^(^#^)^ is specified the default is an optimal bandwidth.

^k^ercode^(^#^)^ specifies the weight function (kernel) to calculate the required
     univariate densities according to the following numerical codes:

 1 = Uniform
  2 = Triangle
  3 = Epanechnikov
  4 = Quartic (Biweight)
  5 = Triweight
  6 = Gaussian
  7 = Cosinus

^np^oint^(^#^)^ specifies the number of equally spaced points (which define a
     grid) in the range of ^xvar^ used for the regression estimation.

^g^en^(^mhvar gridvar^)^ creates two variables containing the estimated regression
     (conditional mean) values and the corresponding grid points, respectively.

^nog^raph suppresses the graph.

graph_options are any of the options allowed with ^graph, twoway^.


Remarks
--------

^k^ercode, and ^np^point are not optional. If the user does not
provide them, the program halts and displays an error message on screen.

This program uses kernel density estimators modified from Salgado-Ugarte,
et al. (1993) and based on the equations provided by Haerdle (1991) and
Scott (1992).

The smoothness of the resulting estimate can be regulated by changing the
bandwidth: wide intervals produce smooth results; narrow intervals give
noisier estimates.

Except for the Gaussian kernel, all the functions are supported on [-1,1].

While using the ^gen^ option, if the number of cases is less than ^np^oint
then the program sets the number of the observations = ^np^oint to obtain the
full set of estimations.

This procedure can be regarded as a descriptive smoother of scatterplots as
well as a nonparametric regression estimator (Nadaraya-Watson).

In the case of optimal bandwidth, the global S_1 keeps the value of the bandwidth.



Examples
---------

  . ^kernreg1 wait dura, bwidth(0.65) kercode(4) npoint(100)^

  . ^kernreg1 accel time, b(2.4) k(4) np(100) gen(m2p4 g2p4) nog^

  . ^kernreg1 postax pretax, k(6) np(100) gen(cm gp) nog^

References
-----------

Chambers, J.M., W.S. Cleveland, B. Kleiner and P.A. Tukey. 1983. Graphical
    methods for data analysis. Wadsworth & Brooks/Cole.

Fox, J. 1990. Describing univariate distributions. In (Fox, J. & J. S. Long,
    eds.) Modern Methods of Data Analysis.  Sage.

Haerdle, W. 1991. Smoothing techniques with implementation in S.
    Springer-Verlag.

Salgado-Ugarte, I.H., M. Shimizu, and T. Taniuchi. 1993. snp6: Exploring the
    shape of univariate data using kernel density estimators. Stata Technical
    Bulletin 16: 8-19.

Salgado-Ugarte, I. H., M. Shimizu, and T. Taniuchi 1995. snp6.1: ASH,
    WARPing, and kernel density estimation for univariate data. Stata
    Technical Bulletin 26: 23-31.

Salgado-Ugarte, I. H., M. Shimizu, and T. Taniuchi 1995. snp6.2: Practical
    rules for bandwidth selection in univariate density estimation. Stata
    Technical Bulletin 27: 5-19.

Scott, D. W. 1992. Multivariate density estimation: Theory, practice,
    and visualization. John Wiley & Sons.

Silverman, B. W. 1986. Density estimation for statistics and data analysis.
    Chapman and Hall.


Author
---------

        Xavi Ramos
        Universitata Autonoma de Barcelona
        Departament d'economia Aplicada
        08193 Bellaterra
        Spain
        xramos@volcano.uab.es

Also see
---------

    STB: STB-30 snp9, STB-27 snp6.2, STB-26 snp6.1, STB-16 snp6
On-line: ^help^ for @kerneld@, @warpden@, @warpdens@, @warpreg@,@gwarpreg@
