Robust Regression via Mutivariate Regression Depth
This addresses robust regression for data with contamination, offering theoretical guarantees but appears incremental as it extends depth-based methods to broader settings.
The paper tackles robust regression under Huber's ε-contamination models by using estimators based on multivariate regression depth functions, showing they achieve minimax rates across various regression problems like nonparametric and sparse linear regression.
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.