Some new normal comparison inequalities related to Gordon’s inequality
Dawei Lu and
Xiaoguang Wang
Statistics & Probability Letters, 2014, vol. 88, issue C, 133-140
Abstract:
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.
Keywords: Gordon’s inequality; Slepian’s inequality; Comparison inequality (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1016/j.spl.2014.02.006
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