Central limit theorem for linear spectral statistics of large dimensional separable sample covariance matrices

被引：10

作者：

Bai, Zhidong ^{[1
,2
]}

Li, Huiqin ^{[3
]}

Pan, Guangming ^{[4
]}

机构：

[1] Northeast Normal Univ, KLASMOE, Changchun 130024, Jilin, Peoples R China

[2] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China

[3] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China

[4] Nanyang Technol Univ, Sch Phys & Mathmat Sci, Div Math Sci, Singapore 637371, Singapore

来源：

BERNOULLI | 2019年 / 25卷 / 03期

关键词：

central limit theorem; linear spectral statistics; random matrix theory; separable sample covariance matrix; EIGENVALUE; PRODUCT; TESTS; RATIO;

D O I：

10.3150/18-BEJ1038

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：

Suppose that X-n = (x(jk)) is N x n whose elements are independent complex variables with mean zero, variance 1. The separable sample covariance matrix is defined as Bn = 1/N T-2n(1/2) XnT1nXn* T-2n(1/2) where T-1n is a Hermitian matrix and T-2n(1/2) is a Hermitian square root of the nonnegative definite Hermitian matrix T-2n. Its linear spectral statistics (LSS) are shown to have Gaussian limits when n/N approaches a positive constant under some conditions.

引用

页码：1838 / 1869

页数：32

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