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April 2016 Nonparametric modal regression
Yen-Chi Chen, Christopher R. Genovese, Ryan J. Tibshirani, Larry Wasserman
Ann. Statist. 44(2): 489-514 (April 2016). DOI: 10.1214/15-AOS1373

Abstract

Modal regression estimates the local modes of the distribution of $Y$ given $X=x$, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usual regression methods. We study a simple nonparametric method for modal regression, based on a kernel density estimate (KDE) of the joint distribution of $Y$ and $X$. We derive asymptotic error bounds for this method, and propose techniques for constructing confidence sets and prediction sets. The latter is used to select the smoothing bandwidth of the underlying KDE. The idea behind modal regression is connected to many others, such as mixture regression and density ridge estimation, and we discuss these ties as well.

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Yen-Chi Chen. Christopher R. Genovese. Ryan J. Tibshirani. Larry Wasserman. "Nonparametric modal regression." Ann. Statist. 44 (2) 489 - 514, April 2016. https://doi.org/10.1214/15-AOS1373

Information

Received: 1 December 2014; Revised: 1 August 2015; Published: April 2016
First available in Project Euclid: 17 March 2016

zbMATH: 1338.62113
MathSciNet: MR3476607
Digital Object Identifier: 10.1214/15-AOS1373

Subjects:
Primary: 62G08
Secondary: 62G05 , 62G20

Keywords: bootstrap , confidence set , mixture model , modes , Nonparametric regression , prediction set

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 2 • April 2016
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