Title: Robust Regression via Mutivariate Regression Depth,
Abstract: 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.