Open Access
May 2020 Robust regression via mutivariate regression depth
Chao Gao
Bernoulli 26(2): 1139-1170 (May 2020). DOI: 10.3150/19-BEJ1144


This paper studies robust regression in the settings of Huber’s $\epsilon$-contamination models. We consider estimators that are maximizers of multivariate regression depth functions. These estimators are shown to achieve minimax rates in the settings of $\epsilon$-contamination models for various regression problems including nonparametric regression, sparse linear regression, reduced rank regression, etc. We also discuss a general notion of depth function for linear operators that has potential applications in robust functional linear regression.


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Chao Gao. "Robust regression via mutivariate regression depth." Bernoulli 26 (2) 1139 - 1170, May 2020.


Received: 1 March 2017; Revised: 1 March 2019; Published: May 2020
First available in Project Euclid: 31 January 2020

zbMATH: 07166559
MathSciNet: MR4058363
Digital Object Identifier: 10.3150/19-BEJ1144

Keywords: contamination model , data depth , high-dimensional regression , Minimax rate , robust statistics

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 2 • May 2020
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