Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.spa.2011.10.002
Title: Convergence rates to the Marchenko-Pastur type distribution
Authors: Bai, Z.
Hu, J.
Zhou, W. 
Keywords: Convergence rate
Sample covariance matrix
Spectral distribution
Issue Date: Jan-2012
Citation: Bai, Z., Hu, J., Zhou, W. (2012-01). Convergence rates to the Marchenko-Pastur type distribution. Stochastic Processes and their Applications 122 (1) : 68-92. ScholarBank@NUS Repository. https://doi.org/10.1016/j.spa.2011.10.002
Abstract: S n = 1 n T 1/2 n X nX n T 1/2 n , where X n = (xi j ) is a p n matrix consisting of independent complex entries with mean zero and variance one, Tn is a p p nonrandom positive definite Hermitian matrix with spectral norm uniformly bounded in p. In this paper, if supn supi, j E | x 8 i j |> ∞ and y n = p/n > 1 uniformly as n → ∞, we obtain that the rate of the expected empirical spectral distribution of Sn converging to its limit spectral distribution is O(n 1/2). Moreover, under the same assumption, we prove that for any < 0, the rates of the convergence of the empirical spectral distribution of Sn in probability and the almost sure convergence are O(n 2/5) and O(n 2/5+) respectively. © 2011 Elsevier B.V. All rights reserved.
Source Title: Stochastic Processes and their Applications
URI: http://scholarbank.nus.edu.sg/handle/10635/105073
ISSN: 03044149
DOI: 10.1016/j.spa.2011.10.002
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

SCOPUSTM   
Citations

6
checked on Dec 3, 2021

WEB OF SCIENCETM
Citations

4
checked on Dec 3, 2021

Page view(s)

150
checked on Dec 2, 2021

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.