在NA样本下一类双边截断型分布族参数的经验Bayes估计

A CLASS OF PROBLEMS OF THE EMPIRICAL BAYES ESTIMATION FOR THE PARAMETER OF THE TWO-SIDE TRUNCATED DISTRIBUTION FAMILIES

在平方损失下,讨论一类双边截断型均匀分布族参数的经验贝叶斯(EB)估计的渐近性。按照贝叶斯(Bayes)方法,导出均匀分布族参数的Bayes估计,利用历史样本,采用概率密度函数的核估计方法,构造出边缘密度函数的估计,从而得到参数的EB估计,在一定的条件下,证明所得到的EB估计是渐近最优的,而且得到了其收敛速度,最后举例说明满足定理条件的参数的先验分布是存在的。

Under the condition of squared loss, we discussed the asymptotic behavior for empirical Bayes （EB） estimation of the parameters of a class of two-side truncated uniform distribution families. We derived the Bayes estimation of the parameters of the family of the Uniform distribution based on the Bayesian methods and constructed the estimate of the marginal density function by historical samples and the method of Kernel estimation of probability density function. Then we get the EB estimation of the parameters. We also proved that the EB estimation was asymptotically optimal under certain conditions. Furthermore, we get the convergence rate. Finally, we get the existences of the prior distribution of the parameters satisfying the condition of the Theorem by example.