一类连续型单参数指数族参数的经验Bayes检验函数的收敛速度

Convergence Rates for Empirical Bayes Test of Parameter for the Continuous One-parameter Exponential Family

本文研究了一类连续型单参数指数族参数的经验Bayes检验问题.利用独立同分布样本下概率密度函数的递归核估计和Bayes检验函数的单调性,重新构造一类连续型单参数指数族参数的EB检验函数.通过修改EB检验函数的构造方法,构造了单调的Bayes检验函数.在一定的条件下,获得了EB检验函数的收敛速度,改进了现有文献中的收敛速度阶的结果.最后给出满足定理条件的数值算例.

The empirical Bayes test problem of parameter for a class of continuous one-parameter exponential family is considered in this paper.By using the recursive kernel esti-mation of probability density function and monotonicity of Bayes test function in the case of independent and identically distributed samples,the EB test function in established for a class of continuous one-parameter exponential family.By the construction method of modifying EB test function,the monotone Bayes test function are constructed.In addition,convergence rates of EB test function are obtained under the suitable conditions,and the results of convergence rate order are improved.Finally,a numerical example is presented to verify the conditions of the theorem.