Statistics and Its Interface
Volume 8 (2015)
Special Issue on Extreme Theory and Application (Part II)
Guest Editors: Yazhen Wang and Zhengjun Zhang
Kernel-type estimator of the mean for a heavy tailed distribution
Pages: 85 – 91
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.
mean, heavy tails, kernel-type estimator, extreme quantile, reduced bias