CONVERGENCE RATE OF EXPECTED SPECTRAL DISTRIBUTIONS OF LARGE RANDOM MATRICES .2. SAMPLE COVARIANCE MATRICES

被引：58

作者：

BAI, ZD

机构：

来源：

ANNALS OF PROBABILITY | 1993年 / 21卷 / 02期

关键词：

BERRY-ESSEEN INEQUALITY; CONVERGENCE RATE; LARGE DIMENSIONAL RANDOM MATRIX; MARCHENKO-PASTUR DISTRIBUTION; SAMPLE COVARIANCE MATRIX; SEMICIRCULAR LAW; SPECTRAL ANALYSIS; STIELTJES TRANSFORM; WIGNER MATRIX;

D O I：

10.1214/aop/1176989262

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：

In the first part of the paper, we developed 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.

引用

页码：649 / 672

页数：24

共 5 条

[1] CONVERGENCE RATE OF EXPECTED SPECTRAL DISTRIBUTIONS OF LARGE RANDOM MATRICES .1. WIGNER MATRICES [J].