The study on Empirical Bayes Procedure for Selecting the Best Normal Population

碩士論文[[abstract]]於本文中，我們在貝氏的架構下，利用經驗貝氏法來解決擇優問題。我們所探討的問題是：假設k 個母體 ，而 ，之分配為常態分配 ，其參數 及 是未知的，且具有某種事前機率分配，在給定兩個控制值 與 之情況下，我們想從合格子集中，選出平均數最接近目標值的母體。而所謂「合格子集」，即此k個母體中其相關參數 且 介於 與 之間所有母體所成之集合。明顯地，在論文中我們所要探討的擇優問題會涉及兩個參數及三項準則。而如何找到一個平均數最接近目標值，但變異數不至於過大的母體將是我們的目標。 相關的經驗貝氏擇優規則已被提出，我們也證明其漸進最適性。並且我們也從事小樣本的模擬研究，來探討經驗貝氏擇優規則之行為表現，並獲得不錯的結果。[[abstract]]In this paper, we use empirical Bayes approach to solve the selecting problem under Bayes framework. We focus on selecting the best population from k Normal population with some prior. Consider k population .Each population has a normal distribution , whose parameters and are unknown. For given control values and ,we are interested in selecting some population whose mean is the closest to the target in the qualified subset in which each parameter and is between and .Clearly ,in this paper , it involves two parameter and three criteria in the selecting problem. In this paper, an empirical Bayes rule would be proposed, and the asymptotical optimality of the proposed would be proved. At the same time, some Monte Carlo simulation will be done to discover the behavior of the proposed rule and by the approach we get well result