| Summary: | 博士 === 淡江大學 === 數學學系 === 87 === In many practical occasions, an experimenter often faces with the situation of testing for homogeneity. And when the hypothesis of homogeneity is rejected, the experimenter often needs to rank priority of several categories or treatments under consideration according to his goal. This concerns the multiple comparison of ranking and selection which has been developed in last forty years. Readers are referred to Gupta and Panchaphesan (1979), for instance, among others.
In this area of ranking and selection, most literature are concerned with one criterion, for example, a population is considered as the best if it is associated with some largest (or smallest) parameter in a finite set of populations. In many situations, it may not satisfy the experimenter''s demand. For example, in industrial statistics, one needs not only to attain its largest target, but on the other hands, one also needs to keep the variation of product under control. Under this circumstance, a single criterion for selection of potential treatments does not meet our requirement. Recently, Gupta, Liang and Rau(1994) consider selecting the best normal population compared with a control. It involves two criteria for selection, however, they belong to same character and only the location parameter is concerned. For this consideration, we consider selecting the best population compared with two controls. Obviously, we consider two main different quantities, i.e. mean and variance for our main concern in the selection problem.
Shortly speaking, in this thesis we consider k(k 2) populations whose mean and variance are all unknown. For given two control values and , we are interested in selecting some population whose mean is the largest in the qualified subset in which each mean is larger than or equal to and whose variance is less than or equal to . In a Bayes framework, we focus on the normal populations with some conjugate prior in this thesis. However, the analogous method can be applied for the cases other than normal. A Bayes approach is set up and an empirical Bayes procedure is proposed which has been shown to be asymptotically optimal.
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