In this paper,we obtain empirical Bayes（EB）procedures for selecting the bestamong k different exponential populations（the form of the conditional probability densitye.g.each population is f<sub>4</sub>...In this paper,we obtain empirical Bayes（EB）procedures for selecting the bestamong k different exponential populations（the form of the conditional probability densitye.g.each population is f<sub>4</sub>（x<sub>i</sub>/b<sub>i</sub>）=b<sub>i</sub> exp（-b<sub>i</sub>x<sub>i</sub>）,x<sub>i</sub>,b<sub>i</sub>∈（0,∞）,i=1,2,…,k）.These rulesare based on the EB estimators of b<sub>i</sub>.We show that,under the squared error loss,the Bayesrisk of the EB estimators converges to the related minimum Bayes risks with rates of conver-gence at Jeast of order O(n<sup>-q</sup>).Further,for the selection problem,the rates of convergenceof the proposed selection rules are shown to be at least of order O(n<sup>（-q）/2</sup> where q can bearbitrarily close to 1/5 or 1 under suitable conditions.展开更多
基金Supported by the National Natural Science Foundation of China
文摘In this paper,we obtain empirical Bayes（EB）procedures for selecting the bestamong k different exponential populations（the form of the conditional probability densitye.g.each population is f<sub>4</sub>（x<sub>i</sub>/b<sub>i</sub>）=b<sub>i</sub> exp（-b<sub>i</sub>x<sub>i</sub>）,x<sub>i</sub>,b<sub>i</sub>∈（0,∞）,i=1,2,…,k）.These rulesare based on the EB estimators of b<sub>i</sub>.We show that,under the squared error loss,the Bayesrisk of the EB estimators converges to the related minimum Bayes risks with rates of conver-gence at Jeast of order O(n<sup>-q</sup>).Further,for the selection problem,the rates of convergenceof the proposed selection rules are shown to be at least of order O(n<sup>（-q）/2</sup> where q can bearbitrarily close to 1/5 or 1 under suitable conditions.
