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标题：Statistics of extremes in athletics
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作者：Lígia Henriques-Rodrigues ; M. Ivette Gomes ; Dinis Pestana. 等
期刊名称：RevStat : Statistical Journal
印刷版ISSN：1645-6726
出版年度：2011
卷号：9
期号：2
出版社：Instituto Nacional de Estatística
摘要：TV shows on any athletic event make clear that those who want gold medals cannot dispense statistics. And the statistics more appealing to champions and coachers are the extreme order statistics, and in particular maximum (or minimum) values and records. The models in statistics of extremes are usually semi-parametric or even non-parametric in nature, with the imposition of a few regularity conditions in the appropriate tail of the unknown model underlying the available data. The primordial parameter is the extreme value index, the shape parameter in the (unified) extreme value distribution. The estimation of the extreme value index is one of the basis for the estimation of other parameters of rare events, like the right endpoint of the model underlying the data, a high quantile, the return period and the probability of exceedance of a high level. In this paper, we are interested in an application of statistics of extremes to the best personal marks in a few athletic events. Due to the way data are collected, we begin with a parametric data analysis, but we pay special attention to the semi-parametric estimation of the extreme value index and the right endpoint whenever finite, the possible world record, given the actual conditions. In order to achieve a better decision we consider a few alternative semi-parametric estimators available in the literature, and heuristic rules for the choice of thresholds.
关键词：statistics of extremes; athletics; semi-parametric estimation; extreme value index; right endpoint; excellence indicators; Monte Carlo methodology.