The Annals of Probability

Convergence Rate of Expected Spectral Distributions of Large Random Matrices. Part II. Sample Covariance Matrices

Z. D. Bai

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Abstract

In the first part of the paper, we develop certain inequalities to bound the difference between distributions in terms of their Stieltjes transforms and established a convergence rate of expected spectral distributions of large Wigner matrices. The second part is devoted to establishing convergence rates for the sample covariance matrices, for the cases where the ratio of the dimension to the degrees of freedom is bounded away from 1 or close to 1, respectively.

Article information

Source
Ann. Probab. Volume 21, Number 2 (1993), 649-672.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176989262

Digital Object Identifier
doi:10.1214/aop/1176989262

Mathematical Reviews number (MathSciNet)
MR1217560

Zentralblatt MATH identifier
0779.60025

JSTOR
links.jstor.org

Subjects
Primary: 60F15: Strong theorems
Secondary: 62F15: Bayesian inference

Keywords
Berry-Esseen inequality convergence rate large dimensional random matrix Marchenko-Pastur distribution sample covariance matrix semicircular law spectral analysis Stieltjes transform Wigner matrix

Citation

Bai, Z. D. Convergence Rate of Expected Spectral Distributions of Large Random Matrices. Part II. Sample Covariance Matrices. Ann. Probab. 21 (1993), no. 2, 649--672. doi:10.1214/aop/1176989262. http://projecteuclid.org/euclid.aop/1176989262.


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See also

  • Part I: Z. D. Bai. Convergence Rate of Expected Spectral Distributions of Large Random Matrices. Part I. Wigner Matrices. Ann. Probab., Volume 21, Number 2 (1993), 625--648.