Robust covariance and scatter matrix estimation under Huber’s contamination model
Mengjie Chen, Chao Gao, Zhao Ren
The Annals of Statistics · 2018 · Volume 46 · Issue 5
Abstract
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.
Keywords
62C20, 62H12, Breakdown point, contamination model, data depth, High-dimensional statistics, Minimax rate, Outliers
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