ROBUST SPARSE COVARIANCE ESTIMATION BY THRESHOLDING TYLER'S M-ESTIMATOR

• 成果类型: Article
• 署名作者: Goes, John; Lerman, Gilad; Nadler, Boaz
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Weizmann Institute of Science
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1793
• 发表日期: 2020
• 页码: 86-110
• 关键词: high-dimensional covariance; multivariate location; Optimal Rates; scatter; CONVERGENCE; efficient; matrices

摘要

Estimating a high-dimensional sparse covariance matrix from a limited number of samples is a fundamental task in contemporary data analysis. Most proposals to date, however, are not robust to outliers or heavy tails. Toward bridging this gap, in this work we consider estimating a sparse shape matrix from n samples following a possibly heavy-tailed elliptical distribution. We propose estimators based on thresholding either Tyler's M-estimator or its regularized variant. We prove that in the joint limit as the dimension p and the sample size n tend to infinity with p / n -> gamma > 0, our estimators are minimax rate optimal. Results on simulated data support our theoretical analysis.