Gaussian fluctuations for sample covariance matrices with dependent data

被引：6

作者：

Friesen, Olga ^{[1
]}

Loewe, Matthias ^{[1
]}

Stolz, Michael ^{[2
]}

机构：

[1] Univ Munster, Fachbereich Math, D-48149 Munster, Germany

[2] Ruhr Univ Bochum, Fak Math, D-44780 Bochum, Germany

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 2013年 / 114卷

关键词：

Random matrices; Sample covariance matrices; Marcenko-Pastur law; Dependent random variables; EIGENVALUES; THEOREMS; LIMIT;

D O I：

10.1016/j.jmva.2012.08.004

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：

It is known (Hofmann-Credner and Stolz (2008) [4]) that the convergence of the mean empirical spectral distribution of a sample covariance matrix W-n = 1/n YnYnt to the Martenko-Pastur law remains unaffected if the rows and columns of Y-n exhibit some dependence, where only the growth of the number of dependent entries, but not the joint distribution of dependent entries needs to be controlled. In this paper we show that the well-known CLT for traces of powers of W-n also extends to the dependent case. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：270 / 287

页数：18

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