A CONCENTRATION OF MEASURE AND RANDOM MATRIX APPROACH TO LARGE-DIMENSIONAL ROBUST STATISTICS

• 成果类型: Article
• 署名作者: Louart, Cosme; Couillet, Romain
• 署名单位: Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1801
• 发表日期: 2022
• 页码: 4737-4762
• 关键词: multivariate location; COVARIANCE-MATRIX; M-ESTIMATORS; optimization

摘要

This article studies the robust covariance matrix estimation of a data collection X = (x1, ... , xn) with xi = /tau izi + m, where zi is an element of Rp is a con-centrated vector (e.g., an elliptical random vector), m is an element of Rp a deterministic signal and tau i is an element of R a scalar perturbation of possibly large amplitude, under the assumption where both n and p are large. This estimator is defined as the fixed point of a function which we show is contracting for a so-called stable semi-metric. We exploit this semi-metric along with concentration of mea-sure arguments to prove the existence and uniqueness of the robust estimator as well as evaluate its limiting spectral distribution.