Kernel-type estimator of the mean for a heavy tailed distribution

In this paper, we focus on the reduced bias of the mean estimator for a heavy-tailed distribution. It is well known that the classical mean estimator introduced by Peng (2001) is seriously biased under the second order regular variation. To reduce bias, many authors have proposed estimators, for both first and second order parameters of the distribution tail. In this work, we define a kernel type estimator for the mean and we propose a reduced bias estimator. The asymptotic distributional properties of our proposed estimators are derived and we compared their performances with other estimators.

Keywords

mean, heavy tails, kernel-type estimator, extreme quantile, reduced bias

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Published 13 February 2015