{smcl} {* *! version 1.1.1}{...} {title:Title} {phang} {bf:kotlarski} {hline 2} Executes deconvolution kernel density estimation and a robust construction of its uniform confidence band. {marker syntax}{...} {title:Syntax} {p 4 17 2} {cmd:kotlarski} {it:x1} {it:x2} {ifin} [{cmd:,} {bf:numx}({it:real}) {bf:domain}({it:real}) {bf:cover}({it:real}) {bf:tp}({it:real}) {bf:order}({it:real}) {bf:grid}({it:real})] {marker description}{...} {title:Description} {phang} {cmd:kotlarski} executes deconvolution kernel density estimation and a robust construction of its uniform confidence band based on {browse "https://qeconomics.org/ojs/index.php/qe/article/view/1560":Kato, Sasaki, and Ura (2021)}. The command requires as input two measurements, {bf:x1} and {bf:x2}, of the unobserved latent variable {bf:x} with classical measurement errors, {bf:e1} = {bf:x1} - {bf:x} and {bf:e2} = {bf:x2} - {bf:x}, respectively. The output consists of a deconvolution kernel density estimate of {it:f}({bf:x}) and their uniform confidence band over a domain of {bf:x}. {phang} FAQ: Why do kotlarski x1 x2 and kotlarski x2 x1 produce different results? Answer: This is because Kotlarski's identity treats x1 and x2 asymmetrically in that x1 is assumed to have the zero mean of its measurement error, while x2 is not. See Assumption 1 in {browse "https://qeconomics.org/ojs/index.php/qe/article/view/1560":Kato, Sasaki, and Ura (2021)}. {marker options}{...} {title:Options} {phang} {phang} {bf:numx({it:real})} sets the number of grid points of {bf:x} for deconvolution kernel density estimation and its uniform confidence band. The default value is {bf: numx(20)}. {phang} {bf:domain({it:real})} sets the domain of deconvolution kernel density estimation and its uniform confidence band. The default value {bf:domain(2)} defines the domain as +/- 2 standard deviations of {bf:x}. {phang} {bf:cover({it:real})} sets the nominal uniform coverage probability for the uniform confidence band. The default value {bf: cover(0.95)} constructs a 95% uniform confidence band. {phang} {bf:tp({it:real})} sets the scale-normalized tuning parameter. Not invoking this option will entail an optimal choice of the tuning parameter. {phang} {bf:order({it:real})} sets the order {bf: q} of the Hermite polynomial basis. The default value is {bf: order(2)}. {phang} {bf:grid({it:real})} sets the size {bf: L} of grid in the frequency domain. The default value is {bf: grid(50)}. {marker examples}{...} {title:Examples} {phang} ({bf:x1982} first measurement of {bf:x}, {bf:x1983} second measurement of {bf:x}){p_end} {phang}Constructing a uniform confidence band in the domain corresponding to +/- 4 standard deviations of {bf:x}: {phang}{cmd:. use "example_1982_1983.dta"}{p_end} {phang}{cmd:. kotlarski x1982 x1983, domain(4)}{p_end} {phang}Construction of a 90% uniform confidence band: {phang}{cmd:. use "example_1982_1983.dta"}{p_end} {phang}{cmd:. kotlarski x1982 x1983, domain(4) cover(0.90)}{p_end} {marker stored}{...} {title:Stored results} {phang} {bf:kotlarski} stores the following in {bf:e()}: {p_end} {phang} Scalars {p_end} {phang2} {bf:r(N)} {space 10}observations {p_end} {phang2} {bf:r(h)} {space 10}tuning parameter {p_end} {phang2} {bf:r(q)} {space 10}order of Hermite polynomial basis {p_end} {phang2} {bf:r(L)} {space 10}grid size in frequency domain {p_end} {phang} Macros {p_end} {phang2} {bf:r(cmd)} {space 8}{bf:kotlarski} {p_end} {phang} Matrices {p_end} {phang2} {bf:r(x)} {space 10}vector of x {p_end} {phang2} {bf:r(fx)} {space 9}vector of density values {p_end} {phang2} {bf:r(lower)} {space 6}confidence band (lower boundary) {p_end} {phang2} {bf:r(upper)} {space 6}confidence band (upper boundary) {p_end} {title:Reference} {p 4 8}Kato, K., Y. Sasaki., and T. Ura 2021. Robust Inference in Deconvolution. {it:Quantitative Economics}, 12 (1): 109-142. {browse "https://qeconomics.org/ojs/index.php/qe/article/view/1560":Link to Paper} {p_end} {title:Authors} {p 4 8}Kengo Kato, Cornell University, Ithaca, NY.{p_end} {p 4 8}Yuya Sasaki, Vanderbilt University, Nashville, TN.{p_end} {p 4 8}Takuya Ura, University of California, Davis, CA.{p_end}