Two Classes Of Extreme Value Index Estimators For Heavy Tailed Distributions

The asymptotic properties of two classes of heavy-tailed extreme value index estima-tors are discussed in this paper.Suppose {Xn,n?1} is an independent and identically distributed sequence of random variables.We use the order statistics X1,n ?…?Xn,n which associated to the sample X1,…,Xn to construct extreme value index estimators.We derived the consistency and asymptotic normality of estimators and used simulation to compare the estimators with several estimators mentioned in this paper.This paper is mainly composed of three parts.In the first part,we construct a class of extreme value index estimators based on the general functional form proposed by Paulauskas and Vaiciulis(2017)[68],and weak consistency and asymptotic distributional representation are presented.What's more,we show the estimators have good robustness properties and derived its reduced bias estimator under the third order condition.In the second part,a class of location invariant semi-parametric estimators of a positive extreme value index>0 is proposed by using the method in Fraga Alves(2001b)[29].Its asymptotic distributional representation was derived,and the optimal choice of the sample fraction by mean squared error for some special cases was discussed.In the third part,we compared the estimators mentioned in this paper under minimum mean squared error criterion.