期刊
ANNALS OF STATISTICS
卷 46, 期 5, 页码 1932-1960出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/17-AOS1607
关键词
Data depth; Minimax rate; high-dimensional statistics; outliers; contamination model; breakdown point
资金
- NSF [DMS-1712957]
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 epsilon-contamination model for estimating covariance/scatter matrices with various structures including bandedness and sparsity.
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