文章基本信息

标题：An overview and open research topics in statistics of univariate extremes
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作者：Jan Beirlant ; Frederico Caeiro ; M. Ivette Gomes . 等
期刊名称：RevStat : Statistical Journal
印刷版ISSN：1645-6726
出版年度：2012
卷号：10
期号：1
出版社：Instituto Nacional de Estatística
摘要：This review paper focuses on statistical issues arising in modeling univariate extremes of a random sample. In the last three decades there has been a shift from the area of parametric statistics of extremes, based on probabilistic asymptotic results in extreme value theory, towards a semi-parametric approach, where the estimation of the right and/or left tail-weight is performed under a quite general framework. But new parametric models can still be of high interest for the analysis of extreme events, if associated with appropriate statistical inference methodologies. After a brief reference to Gumbel¡¯s classical block methodology and later improvements in the parametric framework, we present an overview of the developments on the estimation of parameters of extreme events and testing of extreme value conditions under a semi-parametric framework, and discuss a few challenging open research topics.
关键词：extreme value index; parameters of extreme events; parametric and semi-parametric estimation and testing; statistics of univariate extremes.