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标题：Expansions for the Joint Distribution of the Sample Maximum and Sample Estimate
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作者：Christopher S. Withers Industrial Research Limited ; NEW ZEALAND Saralees Nadarajah University of Manchester, UK
期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2008
卷号：70
期号：01
页码：109--123
出版社：Indian Statistical Institute
摘要：Let Fn be the empirical distribution of a random sample in Rp from a dis- tribution F. Let Mn be the componentwise sample maximum and T(F) a smooth functional in Rq. Let . = T(Fn). We use the conditional Edgeworth expansion for .|(Mn ≤ y) to obtain expansions for the joint distribution of (.,Mn). For T(F) = ¦Ì and ¦Ì2, their degree of dependence as measured by the strong¨Cmixing coefficient (.,Mn) is shown to be O(n.1/2) for a class of distributions associated with the EV3 (Weibull), O(n.1/2 logi n) for two classes associated with the EV1 (Gumbel) and O(ni/.1/2) for a class as- sociated with the EV2 () (Frechet), where i is the degree of T(F), that is i = 1 for ¦Ì and i = 2 for ¦Ì2, = 1 for a class that includes the gamma, and = 1/2 for a class that includes the normal.
关键词：Edgeworth expansions, extreme value distributions, strong mixing coefficient.