Empirical-likelihood-based confidence interval for the mean with a heavy-tailed distribution

被引：25

作者：

Peng, L ^{[1
]}

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

来源：

ANNALS OF STATISTICS | 2004年 / 32卷 / 03期

关键词：

empirical likelihood method; heavy tail; Hill estimator; normal approximation; stable law; tail index;

D O I：

10.1214/009053604000000328

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：

Empirical-likelihood-based confidence intervals for a mean were introduced by Owen [Biometrika 75 (1988) 237-249], where at least a finite second moment is required. This excludes some important distributions, for example, those in the domain of attraction of a stable law with index between 1 and 2. In this article we use a method similar to Qin and Wong [Scand. J. Statist. 23 (1996) 209-219] to derive an empirical-likeillood-based confidence interval for the mean when the underlying distribution has heavy tails. Our method can easily be extended to obtain a confidence interval for any order of moment of a heavy-tailed distribution.

引用

页码：1192 / 1214

页数：23

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