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

共 28 条

[1] Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays [J].

Alon, U ;

Barkai, N ;

Notterman, DA ;

Gish, K ;

Ybarra, S ;

Mack, D ;

Levine, AJ .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1999, 96 (12) :6745-6750

[2]

[Anonymous], 2000, AID MEM LECT AM MATH

[3]

Bai Z, 2010, SPRINGER SER STAT, P1, DOI 10.1007/978-1-4419-0661-8

[4] On the convergence of the spectral empirical process of Wigner matrices [J].

Bai, ZD ;

Yao, J .

BERNOULLI, 2005, 11 (06) :1059-1092

[5]

Bai ZD, 2004, ANN PROBAB, V32, P553

[6] CONVERGENCE TO THE SEMICIRCLE LAW [J].

BAI, ZD ;

YIN, YQ .

ANNALS OF PROBABILITY, 1988, 16 (02) :863-875

[7] CONVERGENCE RATE OF EXPECTED SPECTRAL DISTRIBUTIONS OF LARGE RANDOM MATRICES .1. WIGNER MATRICES [J].

BAI, ZD .

ANNALS OF PROBABILITY, 1993, 21 (02) :625-648

[8] CORRECTIONS TO LRT ON LARGE-DIMENSIONAL COVARIANCE MATRIX BY RMT [J].

Bai, Zhidong ;

Jiang, Dandan ;

Yao, Jian-Feng ;

Zheng, Shurong .

ANNALS OF STATISTICS, 2009, 37 (6B) :3822-3840

[9]

Billingsley P., 1999, CONVERGE PROBAB MEAS, V2nd, DOI DOI 10.1002/9780470316962

[10] A note on testing the covariance matrix for large dimension [J].

Birke, M ;

Dette, H .

STATISTICS & PROBABILITY LETTERS, 2005, 74 (03) :281-289

← 1 2 3 →