Heavy-tailed Extreme Value Index Estimation

Extreme value theory is very important in dealing with rare events.Since that,the esti-mating of extreme index is important.In this paper, we consider two new kinds of esti-mators of the tail indexγ, whereγ>O.We present generalized estimators parametrised in a positive real a,which is more efficient than the Hill estimator for a large region of a.These two estimators are based on the statistics Mnα(κO,κ).Under the first order condi-tion we discuss the weak convergence,and under the second order condition, we discuss the asymptotic distribution of the two estimators.A comparative simulation study is also presented for several models,following an appropriate adaptive procedure.