An asymptotically unbiased minimum density power divergence estimator for the Pareto-tail index

JOURNAL OF MULTIVARIATE ANALYSIS

卷:121

Article

Dierckx, Goedele¹  Goegebeur, Yuri²  Guillou, Armelle^3,4 

[1] Hgsk Univ Brussel, Fac Econ & Management, B-1000 Brussels, Belgium

[2] Univ Southern Denmark, Dept Math & Comp Sci, DK-5230 Odense M, Denmark

[3] Univ Strasbourg, UMR 7501, Inst Rech Math Avancee, F-67084 Strasbourg, France

[4] CNRS, F-67084 Strasbourg, France

关键词: Pareto-type distribution;    Tail index;    Bias-correction;    Density power divergence;   

DOI  :  10.1016/j.jmva.2013.06.011

来源: Elsevier

【 摘 要 】

We introduce a robust and asymptotically unbiased estimator for the tail index of Pareto-type distributions. The estimator is obtained by fitting the extended Pareto distribution to the relative excesses over a high threshold with the minimum density power divergence criterion. Consistency and asymptotic normality of the estimator is established under a second order condition on the distribution underlying the data, and for intermediate sequences of upper order statistics. The finite sample properties of the proposed estimator and some alternatives from the extreme value literature are evaluated by a small simulation experiment involving both uncontaminated and contaminated samples. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free