The Asymptotic Property Of Extreme Value Estimator And Quantile Estimator

This article mainly discusses the asymptotic properties of a class of location invariant heavy-tailed extreme value estimators and two classes of quantile estimators.Suppose{Xn,n≤1}is an independent and identically distributed sequeence of random variables.We ues the order statistics X1,n≤…≤Xn,n which associated to the sample X1,…,Xn to construct extreme value estimators and quantile estimators.We derived the consistency and asymptotic normality of estimators in this article.The article mainly consists of two parts.In the first part,constructing the tail index estimators based on a class of functions proposed by Paulauskas and Vaiciulis(2003)[52],and further investigate the consistency and asymptotic normality of its location invariant estimator.The optimal selection of k0 is discussed based on the minimum mean square error(AMSE).The second part aims to solve two problems commonly encountered in quantile estimation.One is that the estimator no longer has good properties after a linear change in the data,and the other is that the estimator often has a large bias.For quantile estimators that do not have the property of linear variation,this paper introduces the PORT-quantile estimator,namely,the extreme estimator is replaced by the PORT-Hill estimator and PORT-moment estimator.To reduce the large bias in quantile estimator,the quantile estimator combines a second order reduced bias tail estimator.Finally it is proved that the two types of quantile estimators still have consistency,property and asymptotic normality property.