Open Access
October 2018 Robust covariance and scatter matrix estimation under Huber’s contamination model
Mengjie Chen, Chao Gao, Zhao Ren
Ann. Statist. 46(5): 1932-1960 (October 2018). DOI: 10.1214/17-AOS1607


Covariance matrix estimation is one of the most important problems in statistics. To accommodate the complexity of modern datasets, it is desired to have estimation procedures that not only can incorporate the structural assumptions of covariance matrices, but are also robust to outliers from arbitrary sources. In this paper, we define a new concept called matrix depth and then propose a robust covariance matrix estimator by maximizing the empirical depth function. The proposed estimator is shown to achieve minimax optimal rate under Huber’s $\varepsilon$-contamination model for estimating covariance/scatter matrices with various structures including bandedness and sparsity.


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Mengjie Chen. Chao Gao. Zhao Ren. "Robust covariance and scatter matrix estimation under Huber’s contamination model." Ann. Statist. 46 (5) 1932 - 1960, October 2018.


Received: 1 March 2016; Revised: 1 June 2017; Published: October 2018
First available in Project Euclid: 17 August 2018

zbMATH: 06964321
MathSciNet: MR3845006
Digital Object Identifier: 10.1214/17-AOS1607

Primary: 62H12
Secondary: 62C20

Keywords: Breakdown point , contamination model , data depth , High-dimensional statistics , Minimax rate , Outliers

Rights: Copyright © 2018 Institute of Mathematical Statistics

Vol.46 • No. 5 • October 2018
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