Bernoulli

  • Bernoulli
  • Volume 16, Number 4 (2010), 1086-1113.

Functional CLT for sample covariance matrices

Zhidong Bai, Xiaoying Wang, and Wang Zhou

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Abstract

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 $[(1-\sqrt{y})^{2},(1+\sqrt{y})^{2}]$, the support of the Marčenko–Pastur law. We also derive the explicit expressions for asymptotic mean and covariance functions.

Article information

Source
Bernoulli, Volume 16, Number 4 (2010), 1086-1113.

Dates
First available in Project Euclid: 18 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.bj/1290092897

Digital Object Identifier
doi:10.3150/10-BEJ250

Mathematical Reviews number (MathSciNet)
MR2759170

Zentralblatt MATH identifier
1210.60025

Keywords
Bernstein polynomial central limit theorem sample covariance matrices Stieltjes transform

Citation

Bai, Zhidong; Wang, Xiaoying; Zhou, Wang. Functional CLT for sample covariance matrices. Bernoulli 16 (2010), no. 4, 1086--1113. doi:10.3150/10-BEJ250. https://projecteuclid.org/euclid.bj/1290092897


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