Some new normal comparison inequalities related to Gordon’s inequality

Let {ξi,j} and {ηi,j}(1≤i≤n,1≤j≤m) be standard Gaussian random variables. Gordon’s inequality says that if E(ξi,jξi,k)≥E(ηi,jηi,k) for 1≤i≤n,1≤j,k≤m, and E(ξi,jξl,k)≤E(ηi,jηl,k) for 1≤i≠l≤n,1≤j,k≤m, the lower bound P(∪i=1n∩j=1m{ξi,j≤λi,j})/P(∪i=1n∩j=1m{ηi,j≤λi,j}) is at least 1. In this paper, two refinements of upper bound for Gordon’s inequality are given.

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Year of publication:	2014
Authors:	Lu, Dawei ; Wang, Xiaoguang
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 88.2014, C, p. 133-140
Publisher:	Elsevier
Subject:	Gordon’s inequality \| Slepian’s inequality \| Comparison inequality

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011040003