对Jahangir组合式矩估计器的改进

在M.Jahangir以常数为权的组合式矩估计器的基础上,给出一种以函数为权的组合式矩估计器,称为L-J估计器.其中,最优加权函数是根据U估计器与形状参数的单调关系,通过数论网格最优化算法搜索解出.大量仿真实验证实,在对K分布形状参数v大范围的参数估计中,L-J估计器在估计精度上,不但较Jahangir等提出的常数加权组合矩估计器的精度有显著提高,而且可与MLE(Maximum Likelihood Estimator)相当.特别是由于MLE作为渐进无偏估计量,需要充分大的样本长度才能达到最优,这就使得L-J估计器的估计精度可在样本长度较小时优于MLE.此外,L-J估计器无需迭代运算,因而在计算效率上,显著优于现有的ML估计器.

Improvement of Jahangir’s multiple moments estimator

Based on M.Jahangir’s multiple moments estimator using constant weight,a new estimator named L-J estimator was proposed,which consists of multiple moments and uses function weight.The optimum weight function was obtained by the sequential algorithm for optimization according to the monotonic relationship of U-estimator and the shape parameter.A large number of simulation experiments show that the accuracy of L-J estimator is not only higher than that of Jahangir’s multiple estimator using constant weight noticeably,but also it can stand comparison with that of maximum likelihood estimator(MLE).As an asymptotic unbiased estimation,MLE requires sufficient large number of samples to achieve the optimum performance,then it makes that the accuracy of L-J estimator can be better than that of MLE in the case of fewer samples.Moreover,the efficiency of L-J estimator is obviously higher than that of MLE,since there is no iteration to need.