B0731
Title: Robust covariance matrix estimation via matrix depth
Authors: Zhao Ren - University of Pittsburgh (United States) [presenting]
Mengjie Chen - University of North Carolina-Chapel Hill (United States)
Chao Gao - University of Chicago (United States)
Abstract: Covariance matrix estimation is one of the most important problems in statistics. To deal with modern complex data sets, not only we need estimation procedures to take advantage of the structural assumptions of the covariance matrix, it is also important to design methods that are resistant to arbitrary source of outliers. We define a new concept called matrix depth and propose to maximize the empirical matrix depth function to obtain a robust covariance matrix estimator. The proposed estimator is shown to achieve minimax optimal rate under Huber's $\epsilon$-contamination model for estimating covariance/scatter matrices with various structures such as bandedness and sparsity. Competitive numerical results are presented for both simulated and real data examples.
