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

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

2004-06-25

arxiv.org/abs/math/0406523v1

Annals of Statistics 2004, Vol. 32, No. 3, 1192-1214

Mathematics

Statistics Theory

Scientific paper

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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