Gamma-Minimax and Minimax Decision Rules for Comparison of Treatments with a Control.
PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS
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This paper deals with the problem of partitioning treatments in comparison with a standard or control under a decision-theoretic formulations. It is assumed that pi sub i, the ith treatment population, is characterized by a random variable X sub i having strongly unimodal and symmetric density f sub i x-theta sub i, - infinity theta sub i infinity, i 0,1,...,k, where pi sub 0 is the control population. Under the assumptions of a linear loss structure and incomplete prior information about theta sub i, i 0,1,...,k, optimal selection rules are derived for classifying the treatments into superior, equivalent, or inferior groups. These Gamma-minimax rules are compared with Bayes rules for the normal means problem. It is shown that the Gamma-minimax rules compare quite favorably with the Bayes rules. Minimax rules are also derived for the same problem. Author
- Statistics and Probability