## The Annals of Probability

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

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

#### 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**

https://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. https://projecteuclid.org/euclid.aop/1176989262.

#### 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.Project Euclid: euclid.aop/1176989261