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2020 Conditional density estimation with covariate measurement error
Xianzheng Huang, Haiming Zhou
Electron. J. Statist. 14(1): 970-1023 (2020). DOI: 10.1214/20-EJS1688


We consider estimating the density of a response conditioning on an error-prone covariate. Motivated by two existing kernel density estimators in the absence of covariate measurement error, we propose a method to correct the existing estimators for measurement error. Asymptotic properties of the resultant estimators under different types of measurement error distributions are derived. Moreover, we adjust bandwidths readily available from existing bandwidth selection methods developed for error-free data to obtain bandwidths for the new estimators. Extensive simulation studies are carried out to compare the proposed estimators with naive estimators that ignore measurement error, which also provide empirical evidence for the effectiveness of the proposed bandwidth selection methods. A real-life data example is used to illustrate implementation of these methods under practical scenarios. An R package, lpme, is developed for implementing all considered methods, which we demonstrate via an R code example in Appendix B.2.


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Xianzheng Huang. Haiming Zhou. "Conditional density estimation with covariate measurement error." Electron. J. Statist. 14 (1) 970 - 1023, 2020.


Received: 1 June 2019; Published: 2020
First available in Project Euclid: 20 February 2020

zbMATH: 07200223
MathSciNet: MR4066544
Digital Object Identifier: 10.1214/20-EJS1688

Primary: 62G08
Secondary: 62G20

Keywords: bandwidth , bias , Cross validation , deconvoluting kernel


Vol.14 • No. 1 • 2020
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