Rate of convergence in probability to the Marchenko-Pastur law

Friedrich Götze, А. Н. Тихомиров

Type: Article

Publication Date: 2004-06-01

Citations: 83

DOI: https://doi.org/10.3150/bj/1089206408

Abstract

It is shown that the Kolmogorov distance between the spectral distribution function of a random covariance matrix (1/p)XXT, where X is an n×p matrix with independent entries and the distribution function of the Marchenko-Pastur law is of order O(n-1/2) in probability. The bound is explicit and requires that the twelfth moment of the entries of the matrix is uniformly bounded and that p/n is separated from 1.

Locations

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+ PDF Chat	Convergence Rate of Expected Spectral Distributions of Large Random Matrices. Part II. Sample Covariance Matrices	1993	Zhidong Bai
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