Empirical Likelihood Methods with Heavy Tails

Abstract

Heavy tailed distributions have recently appeared in numerous applications: teletraffic data modeling, community size estimation, value-at-risk in finance, etc. For the estimation of the tail index, one of the well-known estimators is the so called Hill estimator. One obvious way to construct a confidence interval for this index is via the normal approximation of the Hill estimator. In the first part of this talk we present an empirical likelihood based confidence interval for the tail index. In the second part we propose an empirical likelihood based confidence interval for the mean when the underlying distribution has heavy tails, which includes the case of infinite variance.