一类位置不变重尾指数估计  

A class of heavy tailed index estimator of location invariant

作　　者：李彤彤[1] 

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《陕西科技大学学报》2017年第3期180-185,共6页Journal of Shaanxi University of Science & Technology

基　　金：教育部人文社会科学研究项目(14YJA790034)

摘　　要：根据M_n^((α))(k_0,k)的收敛性及其渐近展开式,提出一种新的位置不变的极值指数估计量γ_n^((1))(k_0,k,α),并在适当的二阶正规变换的条件下,推导了上述估计量相关的渐近性质,以及门限k_0的最优选择,利用Monte-Carlo对估计量进行了模拟分析,对估计量γ_n^((1))(k_0,k,α)与Fraga Alves提出的估计量γ_n^((H))(k_0,k)进行模拟比较,新提出的估计量表现更好.According to M_n^((α))(k_0,k)the convergence and asymptotic expansion,This paper presents a new location invariant estimator of the extreme value index γ_n^((1))(k_0,k,α),and under the condition of appropriate second order normal transformation,deriving the relevant asymptotic properties of the estimator above,And the optimal choice of threshold k_0,using Monte-Carlo for simulation analysis,simulating and comparing the estimator γ_n^((1))(k_0,k,α)and another estimator γ_n^((H))(k_0,k)which was proposed by Fraga Alves,the new proposed estimator has the better performance.

关 键 词：重尾分布 极值指数 位置不变 正规变化 均方误差 渐近性质 Hill估计 

分 类 号：O212.4[理学—概率论与数理统计]