On the error bound in a combinatorial central limit theorem

被引：22

作者：

Chen, Louis H. Y. ^{[1
]}

Fang, Xiao ^{[2
]}

机构：

[1] Natl Univ Singapore, Dept Math, Singapore 119076, Singapore

[2] Natl Univ Singapore, Dept Stat & Appl Probabil, Singapore 117546, Singapore

来源：

BERNOULLI | 2015年 / 21卷 / 01期

关键词：

combinatorial central limit theorem; concentration inequality; exchangeable pairs; Stein's method; APPROXIMATION; REMAINDER;

D O I：

10.3150/13-BEJ569

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：

Let X = {X-ij: 1 <= i, j <= n} be an n x n array of independent random variables where n >= 2. Let it be a uniform random permutation of {1, 2,... n}, independent of X, and let W = Sigma(n)(i=1) X-i pi(i). Suppose X is standardized so that EW = 0, Var(W) = 1. We prove that the Kolmogorov distance between the distribution of W and the standard normal distribution is bounded by 451 Sigma(n)(i,j=1) E vertical bar X-ij vertical bar(3)/n. Our approach is by Stein's method of exchangeable pairs and the use of a concentration inequality.

引用

页码：335 / 359

页数：25