Asymptotic Properties For A Kind Of Negative Pickands-type Estimator And Smoothing Positive Index Estimator

Two Parts makes up this thesis. The first part is considering the asymptotic expansion and the choice of optimal sample fraction of a kind of Pickands type estimators with negative extreme value index under second regularly varying conditions.In the second part of this paper, a new kind of smoothing estimator for the positive extreme value index is proposed, i.e.whereand t,s∈R,t> s≥1,[x] denotes the smallest integer greater than or equal to x. The asymptotic properties of av(?)_k,n, are obtained by using weak convergence of tail empirical process. Finite sample simulation shows that the proposed smoothing positive index estimator has fine properties compared to non-smoothing estimator (?)_k,n and other smoothing estimators.