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
云南民族大学学报:自然科学版,2016,25(6):516-523

贺园园 HYY

摘要


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〖AKρ^〗n,k(K(1,2),α,t*(ρ,β))与Goegebeur提出的估计量〖AKρ^〗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 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 〖AKρ^〗n,k(K(1,2),α,t*(ρ,β)) with the estimator 〖AKρ^〗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.

参考



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