# Robust Regression via Mutivariate Regression Depth

arXiv: https://arxiv.org/abs/1702.04656 · HTML: https://mlsanity.com/paper/1702.04656/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2017.

## Built on by (most cited first, 20 of 20)

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- [Calibrated Data-Dependent Constraints with Exact Satisfaction Guarantees](https://mlsanity.com/paper/2301.06195/) (2023)
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## Abstract (arXiv)

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.