一类位置不变的极值指数估计量  

A Class of Location-Invariant Extreme Value Index Estimators

作　　者：蒲钰瑶 陈守全[1] PU Yuyao;CHEN Shouquan(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2023年第4期75-79,共5页Journal of Southwest China Normal University(Natural Science Edition)

摘　　要：本文提出了一类位置不变的重尾极值估计量,γ∧n(k_(0),k,r)=1/k_(0)∑_(i=1)^(k_(0))(1/r((X_(n-i,n)-X_(n-k,n)/X_(n-k0,n)-X_(n-k,n))^(r)-1))/1+r/k_(0)∑_(i=1)^(k_(0))(1/r(((X_(n-i,n)-X_(n-k,n))/(X_(n-k 0,n)-X_(n-k,n))^(r)-1))其中:γ>0,k 0是小于k的正整数.得到了此位置不变极值估计量的弱相合性和渐近正态性,并根据其渐近展开式得到k 0的最优选择.In this paper,we propose a class of location-invariant heavy-tailed extreme value estimatorsγ∧n(k_(0),k,r)=1/k_(0)∑_(i=1)^(k_(0))(1/r((X_(n-i,n)-X_(n-k,n)/X_(n-k0,n)-X_(n-k,n))^(r)-1))/1+r/k_(0)∑_(i=1)^(k_(0))(1/r(((X_(n-i,n)-X_(n-k,n))/(X_(n-k 0,n)-X_(n-k,n))^(r)-1))whereγ>0,k 0 is a positive integer less than k.The weak conjunction and asymptotic normality of this location invariant extreme value estimator are obtained,and the optimal choice of k 0 is obtained according to its asymptotic expansion.

关 键 词：重尾估计 二阶正则变换 位置不变 渐近正态性 

分 类 号：O211.4[理学—概率论与数理统计]