ROBUST COVARIANCE AND SCATTER MATRIX ESTIMATION UNDER HUBER'S CONTAMINATION MODEL

• 成果类型: Article
• 署名作者: Chen, Mengjie; Gao, Chao; Ren, Zhao
• 署名单位: University of Chicago; University of Chicago; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1607
• 发表日期: 2018
• 页码: 1932-1960
• 关键词: location-scale depth; Optimal Rates; Adaptive estimation; sparse pca; multivariate scatter; high dimensions; CONVERGENCE; notions

摘要

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.