Robust estimation of high-dimensional covariance and precision matrices

• 成果类型: Article
• 署名作者: Avella-Medina, Marco; Battey, Heather S.; Fan, Jianqing; Li, Quefeng
• 署名单位: Massachusetts Institute of Technology (MIT); Imperial College London; Princeton University; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asy011
• 发表日期: 2018
• 页码: 271284
• 关键词: regularization

摘要

High-dimensional data are often most plausibly generated from distributions with complex structure and leptokurtosis in some or all components. Covariance and precision matrices provide a useful summary of such structure, yet the performance of popular matrix estimators typically hinges upon a sub-Gaussianity assumption. This paper presents robust matrix estimators whose performance is guaranteed for a much richer class of distributions. The proposed estimators, under a bounded fourth moment assumption, achieve the same minimax convergence rates as do existing methods under a sub-Gaussianity assumption. Consistency of the proposed estimators is also established under the weak assumption of bounded 2 + epsilon moments for epsilon is an element of (0, 2). The associated convergence rates depend on epsilon.