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.
Publié le : 1993-04-14
Classification:
Berry-Esseen inequality,
convergence rate,
large dimensional random matrix,
Marchenko-Pastur distribution,
sample covariance matrix,
semicircular law,
spectral analysis,
Stieltjes transform,
Wigner matrix,
60F15,
62F15
@article{1176989262,
author = {Bai, Z. D.},
title = {Convergence Rate of Expected Spectral Distributions of Large Random Matrices. Part II. Sample Covariance Matrices},
journal = {Ann. Probab.},
volume = {21},
number = {4},
year = {1993},
pages = { 649-672},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989262}
}
Bai, Z. D. Convergence Rate of Expected Spectral Distributions of Large Random Matrices. Part II. Sample Covariance Matrices. Ann. Probab., Tome 21 (1993) no. 4, pp. 649-672. http://gdmltest.u-ga.fr/item/1176989262/