几何模型中参数的经验贝叶斯估计的渐近性

THE LARGE SAMPLE CHARACTER OF THE PARAMETER IN GEOMETRIC DISTRIBUTING BY EMPIRICAL BAYES ESTIMATION

依据经验Bayes估计的思想方法,研究在平方损失函数下几何分布中参数的经验Bayes(EB)估计问题。研究过程为:在平方损失函数下求得参数的Bayes估计,在相同的损失函数下,利用频率逼近概率这一事实,构造参数的EB估计,最后证明所得到的EB估计是渐近最优的,收敛速度为o(n-(2s-1)/(2s+1))。

According to the principle and method of Empirical Bayes（EB）,we discuss the parameter estimation problem of non-parametric EB.Firstly,we obtain the Bayes estimation of parameter under the square loss.Secondly,we construct the non-parametric Empirical Bayes estimator of parameter under the same loss function based on the principle of frequency close to probability.Finally,we prove that the proposed estimator was an asymptotical optimal EB estimator and its convergence rate.