重尾分布中二阶参数的渐近无偏估计

基于统计量T_(n,k)(K),先提出二阶参数的有偏估计量,再通过2个有偏估计量的线性组合构造了一类二阶参数的渐近无偏估计.在二阶正则条件下,研究了估计量的相合性;在三阶正则条件下,研究了估计量的渐近正态性.最后通过模拟,在特定条件下,将此无偏估计量ρn,k(K~(1,2),α,t*(ρ,β))与Goegebeur提出的估计量ρ_(n,k)(K~(1,2),α_1,α_2,l)的均值和方差进行模拟比较,结果表明,提出的无偏估计量表现更好.

Asymptotically unbiased estimation of the second-order parameter in the heavy-tailed distribution

Based on the statistics T_(n,k)( K),the paper first puts forward the biased estimator of the second- order parameters,and then through a linear combination of the two biased estimators for a class of the second- order constructs the asymptotically unbiased estimation of parameters. The consistency of the estimation is studied under the second- order regular variable condition,and asymptotic normality is achieved under the third- order condition.At last,through simulation,it compares the unbiased estimator ρ_(n,k)( K~(1,2),α,t*( ρ,β)) with the estimator ρ_(n,k)( K~(1,2),α_1,α_2,l) proposed by Goegebeur et al.( 2010) in terms of mean and variance,and the proposed estimator performs better.