Electronic Journal of Statistics

Nonparametric modal regression in the presence of measurement error

Haiming Zhou and Xianzheng Huang

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Abstract

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.

Article information

Source
Electron. J. Statist., Volume 10, Number 2 (2016), 3579-3620.

Dates
Received: May 2016
First available in Project Euclid: 24 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1479956457

Digital Object Identifier
doi:10.1214/16-EJS1210

Mathematical Reviews number (MathSciNet)
MR3575565

Zentralblatt MATH identifier
1357.62185

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties

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

Citation

Zhou, Haiming; Huang, Xianzheng. Nonparametric modal regression in the presence of measurement error. Electron. J. Statist. 10 (2016), no. 2, 3579--3620. doi:10.1214/16-EJS1210. https://projecteuclid.org/euclid.ejs/1479956457


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