Robust regression via mutivariate regression depth
By Chao Gao. Bernoulli, 2017
54 citations recorded by the source corpus.
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.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/fc6a59ed9ec5caa0ee69ac7213ff3e527066de97
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In Statistics and Probability
- Ilias Diakonikolas
- Alistair Stewart
- Sivaraman Balakrishnan
- Weihao Kong
- Pradeep Ravikumar
- Adarsh Prasad
- Arun Sai Suggala
- Jerry Zheng Li
Citations in the corpus
- Robust estimation via robust gradient estimation (2018, methodology): “A complementary line of recent research [10, 20] has focused on providing minimax upper and lower bounds on the performance of estimators under ǫ-contamination model, without the constraint of computational tractability.”
- Efficient Algorithms and Lower Bounds for Robust Linear Regression (2018, background): “This multiplicative dependence on β 2 is not information-theoretically necessary (see, e.g., [Gao17]).”