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标题：Mean-of-order-p location-invariant extreme value index estimation
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作者：M. Ivette Gomes ; Lígia Henriques-Rodrigues ; B.G. Manjunath 等
期刊名称：RevStat : Statistical Journal
印刷版ISSN：1645-6726
出版年度：2016
卷号：14
期号：3
页码：273-296
出版社：Instituto Nacional de Estatística
摘要：A simple generalisation of the classical Hill estimator of a positive extreme value index (EVI) has been recently introduced in the literature. Indeed, the Hill estimator can be regarded as the logarithm of the mean of order p = 0 of a certain set of statistics. Instead of such a geometric mean, we can more generally consider the mean of order p (MOP) of those statistics, with p real, and even an optimal MOP (OMOP) class of EVI-estimators. These estimators are scale invariant but not location invariant. With PORT standing for peaks over random threshold, new classes of PORT-MOP and PORT-OMOP EVI-estimators are now introduced. These classes are dependent on an extra tuning parameter q, 0 ≤ q < 1, and they are both location and scale invariant, a property also played by the EVI. The asymptotic normal behaviour of those PORT classes is derived. These EVI-estimators are further studied for finite samples, through a Monte-Carlo simulation study. An adequate choice of the tuning parameters under play is put forward, and some concluding remarks are provided.
关键词：bootstrap and/or heuristic threshold selection; heavy tails; location/scale invariant ; semi-parametric estimation; Monte-Carlo simulation; optimal levels; statistics of ex- ; tremes