An essentially complete class of multiple decision procedures |
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Authors: | Shanti S Gupta Deng-Yuang Huang |
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Institution: | Purdue University, West Lafayette, IN 47907, USA;Academia Sinica, Taipei, Taiwan |
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Abstract: | Let π1,…, πk represent k(?2) independent populations. The quality of the ith population πi is characterized by a real-valued parameter θi, usually unknown. We define the best population in terms of a measure of separation between θi's. A selection of a subset containing the best population is called a correct selection (CS). We restrict attention to rules for which the size of the selected subset is controlled at a given point and the infimum of the probability of correct selection over the parameter space is maximized. The main theorem deals with construction of an essentially complete class of selection rules of the above type. Some classical subset selection rules are shown to belong to this class. |
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Keywords: | Primary 62F07 Secondary 62G30 Subset Selection Procedure Generalized Monotone Likelihood Ratio Monotone Selection Rule Normal Means Problem Unequal Sample Sizes |
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