重尾分布中二阶参数的渐近无偏估计

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

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.

Based on the statistics Tn,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 con- structs 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 ρn,k （K（1,2） ,α,t＊ （ρ,β）） with the estimator ρn,k （K（1,2） ,α1 ,α2 ,l） proposed by Goegebeur et al. （2010） in terms of mean and variance, and the proposed estimator performs better.