标题： 基于多变量回归深度的鲁棒回归 显示英文标题

标题： Robust Regression via Mutivariate Regression Depth

摘要： 本文研究了Huber的$\epsilon$-污染模型设置下的鲁棒回归。 我们考虑的是多变量回归深度函数的最大化估计量。 这些估计量在各种回归问题中被证明在$\epsilon$-污染模型设置下能达到最小最大率，包括非参数回归、稀疏线性回归、降秩回归等。 我们还讨论了线性算子的一般深度函数概念，该概念在鲁棒函数线性回归中具有潜在应用。 显示英文摘要

摘要： 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.