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.
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页码：1838 / 1869
页数：32
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