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 Electronic Journal of Statistics > Vol. 2 (2008) open journal systems 


A class of unbiased location invariant Hill-type estimators for heavy tailed distributions

Jiaona Li, School of Mathematics and Statistics, Southwest University, Chongqing, 400715
Zuoxiang Peng, School of Mathematics and Statistics, Southwest University, Chongqing, 400715
Saralees Nadarajah


Abstract
Based on the methods provided in Caeiro and Gomes (2002) and Fraga Alves (2001), a new class of location invariant Hill-type estimators is derived in this paper. Its asymptotic distributional representation and asymptotic normality are presented, and the optimal choice of sample fraction by Mean Squared Error is also discussed for some special cases. Finally comparison studies are provided for some familiar models by Monte Carlo simulations.

AMS 2000 subject classifications: Primary 62G32; secondary 65C05.

Keywords: Asymptotic normality, Location invariant Hilltype heavy tailed index estimator, Second order regular variation.

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Li, Jiaona, Peng, Zuoxiang, Nadarajah, Saralees, A class of unbiased location invariant Hill-type estimators for heavy tailed distributions, Electronic Journal of Statistics, 2, (2008), 829-847 (electronic). DOI: 10.1214/08-EJS276.

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Electronic Journal of Statistics. ISSN: 1935-7524