The Annals of Statistics
- Ann. Statist.
- Volume 46, Number 5 (2018), 1932-1960.
Robust covariance and scatter matrix estimation under Huber’s contamination model
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.
Ann. Statist., Volume 46, Number 5 (2018), 1932-1960.
Received: March 2016
Revised: June 2017
First available in Project Euclid: 17 August 2018
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Chen, Mengjie; Gao, Chao; Ren, Zhao. Robust covariance and scatter matrix estimation under Huber’s contamination model. Ann. Statist. 46 (2018), no. 5, 1932--1960. doi:10.1214/17-AOS1607. https://projecteuclid.org/euclid.aos/1534492824
- Supplement to “Robust covariance and scatter matrix estimation under Huber’s contamination model”. In this supplement, we collect the proofs for the remaining main results, provide details on the extension to the noncentered observations and demonstrate numerical studies in low-to-moderate dimensional settings.