An Essentially Complete Class of Multiple Decision Procedures.
PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS
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Let pi sub 1,..., pi sub k represent k or 2 independent populations. The quality of the ith population pi sub i is characterized by a real-valued parameter theta sub i, usually unknown. Define the best population in terms of a measure of separation between theta sub is. A selection of a subset containing the best population is called a correct selection CS. 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.
- Statistics and Probability