  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.
