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

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

2008-09-23

arxiv.org/abs/0809.3869v1

Electronic Journal of Statistics 2008, Vol. 2, 829-847

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/08-EJS276 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

10.1214/08-EJS276

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.

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