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Indexed by:期刊论文

Date of Publication:2014-05-01

Journal:STATISTICS & PROBABILITY LETTERS

Included Journals:SCIE、Scopus

Volume:88

Issue:1

Page Number:133-140

ISSN No.:0167-7152

Key Words:Gordon's inequality; Slepian's inequality; Comparison inequality

Abstract:Let {xi(i,j)} and {eta(iota,j)}(1 <= i <= n, 1 <= j <= m) be standard Gaussian random variables. Gordon's inequality says that if E(xi(i,j)xi(i,k)) >= E(eta(i,j)eta(i,k)) for 1 <= i <= n, 1 <= j, k <= m, and E(xi(i,j)xi(l,k)) <= E(eta(i,j)eta(l,k)) for 1 <= i not equal l <= n, 1 <= j, k <= m, the lower bound P(boolean OR(n)(i=1) boolean AND(m)(j=1) {xi(i,j) <= lambda(i,j)})/P/(boolean OR(n)(i=1) boolean AND(m)(j=1)) {eta(i,j) <= lambda(i,j)}) is at least 1. In this paper, two refinements of upper bound for Gordon's inequality are given. (C) 2014 Elsevier B.V. All rights reserved.