Heavy Tail Index Estimators Based On Block Method And Record Value

Tail index estimation constitutes an important part in the study of extreme value theory.Many classical heavy tail index estimators have been proposed,such as Hill estimator based on order statistics.Pickands estimator based on position invariance and DPR's estimator based on block method.This thesis firstly introduce a new heavy-tailed index estimator in block method.Then propose a new heavy-tailed index estimator which is constructed on the basis of record value.The full text mainly includes two parts:In the first part,a new heavy-tailed index estimator ?(k,s)is proposed in block method.Then its asymptotic consistency under specific conditions and asymptotic normality under second-order regularly varying condition are studied.Finally.Monte-Carlo method is used to simulate and analyze the new estimator when the sample is distributed by four different distribution functions Pareto,Frechet GPD and Burr distribution respectively.By comparing with the estimator proposed by Li J.and Peng Z.[34],the estimator is evaluated from the view of mean value and mean square error.In the second part,a new heavy-tailed index estimator based on record value ?n is proposed,and its consistency under specific conditions and asymptotic normality under second-order regularly varying condition are discussed.Finally,Monte-Carlo method is used to simulate and analyze the new estimator.The numerical results include mean square error,asymptotic standard error and 95%confidence interval under four different distribution functions are given.