Functional CLT for sample covariance matrices

被引：17

作者：

Bai, Zhidong ^{[1
,2
,3
]}

Wang, Xiaoying ^{[4
]}

Zhou, Wang ^{[3
]}

机构：

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

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

[3] Natl Univ Singapore, Dept Stat & Appl Probabil, Singapore 117546, Singapore

[4] N China Elect Power Univ, Sch Math & Phys, Beijing 102206, Peoples R China

来源：

BERNOULLI | 2010年 / 16卷 / 04期

关键词：

Bernstein polynomial; central limit theorem; sample covariance matrices; Stieltjes transform; LIMITING SPECTRAL DISTRIBUTION; CONVERGENCE RATE; DISTRIBUTIONS; EIGENVALUES;

D O I：

10.3150/10-BEJ250

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：

Using Bernstein polynomial approximations, we prove the central limit theorem for linear spectral statistics of sample covariance matrices, indexed by a set of functions with continuous fourth order derivatives on an open interval including [(1 - root y)(2), (1 + root y)(2)], the support of the Marcenko-Pastur law. We also derive the explicit expressions for asymptotic mean and covariance functions.

引用

页码：1086 / 1113

页数：28

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