A CLT FOR REGULARIZED SAMPLE COVARIANCE MATRICES
成果类型：
Article
署名作者：
Anderson, Greg W.; Zeitouni, Ofer
署名单位：
University of Minnesota System; University of Minnesota Twin Cities
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/07-AOS503
发表日期：
2008
页码：
2553-2576
关键词：
摘要：
We consider the spectral properties of a class of regularized estimators of (large) empirical covariance matrices corresponding to stationary (but not necessarily Gaussian) sequences, obtained by banding. We prove a law of large numbers (similar to that proved in the Gaussian case by Bickel and Levina), which implies that the spectrum of a banded empirical covariance matrix is an efficient estimator. Our main result is a central limit theorem in the same regime, which to our knowledge is new, even in the Gaussian setup.