文章基本信息

标题：Stochastic domination and weak convergence of conditioned Bernoulli random vectors
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作者：Erik I. Broman ; Tim van de Brug ; Wouter Kager 等
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2012
卷号：IX
期号：2
页码：403-434
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：For n ≥ 1 let Xn be a vector of n independent Bernoulli randomvariables. We assume that Xn consists of M “blocks” such that the Bernoullirandom variables in block i have success probability pi. Here M does not dependon n and the size of each block is essentially linear in n. Let ˜X n be a randomvector having the conditional distribution of Xn, conditioned on the total numberof successes being at least kn, where kn is also essentially linear in n. Define ˜ Y nsimilarly, but with success probabilities qi ≥ pi. We prove that the law of ˜X nconverges weakly to a distribution that we can describe precisely. We then provethat supP( ˜X n ≤ ˜ Y n) converges to a constant, where the supremum is taken overall possible couplings of ˜X n and ˜ Y n. This constant is expressed explicitly in termsof the parameters of the system.
关键词：Bernoulli random vectors; weak convergence; stochastic domination;conditional distributions; coupling.