Convergence rates of spectral distributions of large sample covariance matrices

被引:24
作者
Bai, ZD [1 ]
Miao, BQ
Yao, JF
机构
[1] NE Normal Univ, Dept Math, Changchun 130024, Peoples R China
[2] Natl Univ Singapore, Dept Stat & Appl Probabil, Singapore 117543, Singapore
[3] Univ Sci & Technol China, Dept Stat & Finance, Hefei 230026, Anhui, Peoples R China
[4] Univ Rennes 1, IRMAR, F-35042 Rennes, France
关键词
convergence rate; random matrix; spectral distribution; Marcenko-Pastur distribution;
D O I
10.1137/S0895479801385116
中图分类号
O29 [应用数学];
学科分类号
070104 [应用数学];
摘要
In this paper, we improve known results on the convergence rates of spectral distributions of large-dimensional sample covariance matrices of size p x n. Using the Stieltjes transform, we first prove that the expected spectral distribution converges to the limiting Marcenko-Pastur distribution with the dimension sample size ratio y = y(n) = p/n at a rate of O(n(-1/2)) if y keeps away from 0 and 1, under the assumption that the entries have a finite eighth moment. Furthermore, the rates for both the convergence in probability and the almost sure convergence are shown to be Op(n(-2/5)) and o(a.s.)(n(-2/5+eta)), respectively, when y is away from 1. It is interesting that the rate in all senses is O(n(-1/8)) when y is close to 1.
引用
收藏
页码:105 / 127
页数:23
相关论文
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