Nonparametric modal regression in the presence of measurement error. (English) Zbl 1357.62185

Zhou, Haiming; Huang, Xianzheng

Electron. J. Stat. 10, No. 2, 3579-3620 (2016).

Summary: 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.

MSC:

62G08	Nonparametric regression and quantile regression
62G20	Asymptotic properties of nonparametric inference
62J05	Linear regression; mixed models

Keywords:

bandwidth selection; deconvoluting kernel; Fourier transform; local mode; mean-shift algorithm; numerical studies