Laboratory of Applied Mathematics, Mohamed Khider University of Biskra, 07000 Biskra, Algeria
Copyright © 2010 Abdelhakim Necir and Djamel Meraghni. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
-functionals summarize numerous statistical parameters and actuarial risk
measures. Their sample estimators are linear combinations of order statistics
(-statistics). There exists a class of heavy-tailed distributions for which the
asymptotic normality of these estimators cannot be obtained by classical results.
In this paper we propose, by means of extreme value theory, alternative
estimators for -functionals and establish their asymptotic normality. Our
results may be applied to estimate the trimmed -moments and financial risk
measures for heavy-tailed distributions.