CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size

被引：13

作者：

Chen, Binbin ^{[1
]}

Pan, Guangming ^{[1
]}

机构：

[1] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 639798, Singapore

来源：

BERNOULLI | 2015年 / 21卷 / 02期

关键词：

central limit theorem; empirical spectral distribution; hypothesis test; linear spectral statistics; sample covariance matrix; CONVERGENCE; TESTS; CLASSIFICATION;

D O I：

10.3150/14-BEJ599

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let A = 1/root np ((XX)-X-T - pI(n)) where X is a p x n matrix, consisting of independent and identically distributed (i.i.d.) real random variables X-ij with mean zero and variance one. When p / n -> infinity, under fourth moment conditions a central limit theorem (CLT) for linear spectral statistics (LSS) of A defined by the eigenvalues is established. We also explore its applications in testing whether a population covariance matrix is an identity matrix.

引用

页码：1089 / 1133

页数：45

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