Three Classes Of Estimators For Extreme Value Index Under Random Right Censoring

A lot of estimators for extreme value index according to the completely observed samples have been put forward by many scholars,whose asymptotic properties have been proven good.However,these biases and mean square errors of the existing estimators for censored samples will increase sharply when the sample data from the heavy-tailed distribution is randomly right-censored.Therefore,three classes of extreme value index estimators based on randomly right-censored samples will be proposed in this paper.This paper is composed of four parts.Inspired by the method that is proposed by Gomes and Martins [32] to construct the generalized Hill estimator,the first part adds a new parameter ?(?? 1)to the two existing censored estimators given by Worms and Worms [45],and the first and second classes of extreme value index estimators are proposed.Then,on the basis of the second class of estimator,the third class of estimator is constructed from the perspective of reducing the bias.The second part gives the asymptotic normality of the first class of estimator when the sample is lightly censored,and the asymptotic normality of the quantile estimator corresponding to the first class of estimator is presented.The third part discusses the asymptotic normality of the second and third classes of estimators when the sample are lightly censored,and the asymptotic normality of the quantile estimator corresponding to the second class of estimator is also presented.In the fourth part,numerical simulation is carried out.Firstly,we theoretically select the range of that can effectively reduce the asymptotic biases of the three classes of estimators,then we make some images to show the biases and mean square errors when the finite samples are lightly censored and heavily censored.Compared with the existing censored estimators,when the appropriate range is selected and the samples are lightly censored,three classes of estimators proposed in this paper are actually biasreduced estimators.In the case of heavily censored samples,the third class of estimator is the most ideal class to reduce the bias.