上次序统计量个数的渐近最优选取  

An asymptotically optimal way to choose the number of upper order statistics

作　　者：何腊梅[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2011年第6期1239-1244,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：四川省重点实验室开放基金资助项目(scsxdz2011006)

摘　　要：有关极值指数的估计方法不少,其中最著名的估计方法之一是Pickands型估计量.由于估计量都是基于次序统计量来构建的,所以估计量所包含的上次序统计量的个数的选取就是一个值得探讨的问题.基于作者曾经提出的一类新的Pickands型估计量,在一定的正则变换条件下,本文给出了该估计量的渐近展式,进而在渐近均方误差最小的准则下给出了上次序统计量个数的最优选取.There are some methods to estimate the extreme value index. One of the most famous methods is Pickands＇estimator which based on order statistics. Therefore a topic on the optimal choice for the number of upper order statistics in estimation of the extreme value index is very important. An asymptotic expansion of a new Pickands＇ estimator is obtained under regular variation condition. Moreover, a method to choose the asymptotically optimal number of upper order statistics involved in the new Pickands＇estimator is presented.

关 键 词：极值指数 Pickands型估计 渐近展式 正则变换 

分 类 号：O211.4[理学—概率论与数理统计]