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

• 成果类型: Article
• 署名作者: Peng, L
• 署名单位: University System of Georgia; Georgia Institute of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000000328
• 发表日期: 2004
• 页码: 1192-1214
• 关键词: Bootstrap; sums

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.