On large deviation for extremes

被引：13

作者：

Drees, H

de Haan, L

Li, DY

机构：

[1] Univ Saarland, Dept Math, D-66041 Saarbrucken, Germany

[2] Erasmus Univ, Fac Econ, Dept Econometr, NL-3000 DR Rotterdam, Netherlands

来源：

STATISTICS & PROBABILITY LETTERS | 2003年 / 64卷 / 01期

关键词：

extremes; extreme value distribution; large deviations; maxima; second order condition; tail empirical distribution function; weighted approximation;

D O I：

10.1016/S0167-7152(03)00130-5

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Recently, a weighted approximation for the tail empirical distribution function has been developed (Approximations to the tail empirical distribution function with application to testing extreme value conditions. preprint, submitted for publication). We show that the same result can also be used to improve a known uniform approximation of the distribution of the maximum of a random sample. From this a general result about large deviations of this maximum is derived. In addition, the relationship between two second-order conditions used in extreme value theory is clarified. (C) 2003 Elsevier B.V. All rights reserved.

引用

页码：51 / 62

页数：12