Open Access
Translator Disclaimer
2016 Nonparametric modal regression in the presence of measurement error
Haiming Zhou, Xianzheng Huang
Electron. J. Statist. 10(2): 3579-3620 (2016). DOI: 10.1214/16-EJS1210


In the context of regressing a response $Y$ on a predictor $X$, we consider estimating the local modes of the distribution of $Y$ given $X=x$ when $X$ is prone to measurement error. We propose two nonparametric estimation methods, with one based on estimating the joint density of $(X,Y)$ in the presence of measurement error, and the other built upon estimating the conditional density of $Y$ given $X=x$ using error-prone data. We study the asymptotic properties of each proposed mode estimator, and provide implementation details including the mean-shift algorithm for mode seeking and bandwidth selection. Numerical studies are presented to compare the proposed methods with an existing mode estimation method developed for error-free data naively applied to error-prone data.


Download Citation

Haiming Zhou. Xianzheng Huang. "Nonparametric modal regression in the presence of measurement error." Electron. J. Statist. 10 (2) 3579 - 3620, 2016.


Received: 1 May 2016; Published: 2016
First available in Project Euclid: 24 November 2016

zbMATH: 1357.62185
MathSciNet: MR3575565
Digital Object Identifier: 10.1214/16-EJS1210

Primary: 62G08
Secondary: 62G20

Keywords: Bandwidth selection , deconvoluting kernel , Fourier transform , local mode , mean-shift algorithm

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.10 • No. 2 • 2016
Back to Top