Empirical-likelihood-based confidence interval for the mean with a heavy-tailed distribution
Statistics Theory
2007-06-13 v1 Statistics Theory
Abstract
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.
Cite
@article{arxiv.math/0406523,
title = {Empirical-likelihood-based confidence interval for the mean with a heavy-tailed distribution},
author = {Liang Peng},
journal= {arXiv preprint arXiv:math/0406523},
year = {2007}
}