Gamma分布族尺度参数的经验贝叶斯单边检验

Empirical Bayes one-sided tests for scale parameter of Gamma distribution family

文章在独立同分布条件下研究了Gamma分布族尺度参数的经验贝叶斯检验问题,在假设贝叶斯检验函数的临界点是属于已知闭区间的前提下,构造了尺度参数的经验贝叶斯检验函数,并证明了其渐近最优性,在合适的条件下获得了O(n-1)的收敛速度,最后给出了一个满足条件的例子。

Empirical Bayes test problems of scale parameter of Gamma distribution family in the case of independent identically distributed samples are studied. Under the assumption that the critical point of Bayes test function is within some known compact interval, an empirical Bayes test function for scale parameter is constructed. The asymptotic optimality is proved and a rate of convergence of order O（n^-1） is achieved in a suitable condition. An example which satisfies the condition is presented.