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June 2004 Empirical-likelihood-based confidence interval for the mean with a heavy-tailed distribution
Liang Peng
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Ann. Statist. 32(3): 1192-1214 (June 2004). DOI: 10.1214/009053604000000328


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-likelihood-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.


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Liang Peng. "Empirical-likelihood-based confidence interval for the mean with a heavy-tailed distribution." Ann. Statist. 32 (3) 1192 - 1214, June 2004.


Published: June 2004
First available in Project Euclid: 24 May 2004

zbMATH: 1091.62038
MathSciNet: MR2065202
Digital Object Identifier: 10.1214/009053604000000328

Primary: 62G15
Secondary: 62G30

Keywords: Empirical likelihood method , heavy tail , Hill estimator , Normal approximation , Stable law , tail index

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 3 • June 2004
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