A Class Of Generalized Location Invariant Hill-type Estimator

Extreme value theory(EVT)is widely used in the analysis of small probability events,the characteristic of peak and thick tail is prominent in the data of financial time series,intuitively,the probability that the data appears at extreme values is larger than the normal distribution,the extreme value theory has obvious advantage to explain this kind of phenomenon.Today,the application of extreme value theory has been expanded and has been widely used in the fields such as nature,economic and financial,insurance,communication and other fields.There are countless studies around the extreme value theory,and the corresponding estimators of extreme value index have been paid close attentions by scholars.The opening of the article leads to the research progress of extreme value theory,the basic knowledge and research significance of extreme value theory and some common extreme value in-dex estimators are briefly reviewed,and several definitions of heavy tailed distribution and various conditions of regular variation are also given;than based on the convergence and asymptotic ex-pansion of the statistic Mn(?)(k0,k),this paper proposes a class of generalized location invariant Hill-type estimator-GLIHE,and proves the consistency and discusses the asymptotic normality of the estimator under second order regular variation;next,discussing the optimal selection of threshold k0 in the sense of mean square error,analysing the selection method of tuning parameter a by using asymptotic relative efficiency rule;in the end,three types of different heavy tailed distribution are used as models,using Monte-Carlo technology to imitate,giving the simulated images of mean value and MSE of the new estimator and the classical location invariant estimator ?nH(k0,k)proposed by Fraga Alves.The results show that the new estimator is more effective than ?nH(k0,k).