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.
Publié le : 2004-06-14
Classification:
Empirical likelihood method,
heavy tail,
Hill estimator,
normal approximation,
stable law,
tail index,
62G15,
62G30
@article{1085408499,
author = {Peng, Liang},
title = {Empirical-likelihood-based confidence interval for the mean with a heavy-tailed distribution},
journal = {Ann. Statist.},
volume = {32},
number = {1},
year = {2004},
pages = { 1192-1214},
language = {en},
url = {http://dml.mathdoc.fr/item/1085408499}
}
Peng, Liang. Empirical-likelihood-based confidence interval for the mean with a heavy-tailed distribution. Ann. Statist., Tome 32 (2004) no. 1, pp. 1192-1214. http://gdmltest.u-ga.fr/item/1085408499/