Robust Regression via Mutivariate Regression Depth

02/15/2017

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by   Chao Gao, et al.

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This paper studies robust regression in the settings of Huber's ϵ-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 ϵ-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.