一类新的极值指数估计  

A New Class of Estimators for Extreme Value Index

作　　者：常帅[1] CHANG Shuai(Department of Mathematics,Taiyuan Normal University,Jinzhong 030619,China)

机构地区：[1]太原师范学院数学系,山西晋中030619

出　　处：《应用数学》2021年第3期515-524,共10页Mathematica Applicata

基　　金：Supported by the Natural Science Foundation of China (11401424);the Natural Science Foundation of Shanxi Province (201801D121022);the Natural Science Foundation for Young Scientists of Shanxi Province (201901D211423);the Taiyuan Normal University Undergraduate Training Program for Innovation and Entrepreneurship (CXCY2078)。

摘　　要：本文提出一类新的极值指数的估计,在一阶与二阶条件下,证明所提出估计具有相合性与渐近正态性.尽管新的估计与L_p估计具有相同的渐近行为,但是新的估计构造相当简单,而且在有限样本下,同一水平进行比较,新的估计表现好于L_p估计.同时,利用Monte-Carlo模拟,在最优水平下,与矩估计和混合矩估计进行比较,新的估计具有一定的优势.In this paper,a new class of extreme value index(EVI)estimators as a generation of the Hill estimator is proposed.Under the first-order condition and secondorder condition,we prove that the introduced estimators are consistent and asymptotically normal.Although new EVI-estimators and Lp EVI-estimators have the same asymptotic behaviour,the form of new EVI-estimators is simple.And the performance of new EVI-estimators is slightly better than that of Lp EVI-estimators at the same level in the finite samples.Meanwhile,we compare new EVI-estimators with moment estimator and mixed-moment estimator in the optimal level by means of Monte-Carlo simulation.It is concluded that new EVI-estimators have a better competitiveness.

关 键 词：重尾 极值指数估计 二阶条件 渐近正态性 

分 类 号：O212[理学—概率论与数理统计]