On Some Multiple Decision Problems
PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS
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This thesis deals with some selection and ranking procedures for restricted families of probability distributions. A selection rule is proposed for distributions which are convex-ordered with respect to a specified distribution G. Some properties of this selection rule are derived. The asymptotic relative efficiencies of this rule with respect to other selection rules are evaluated. A selection rule is also proposed and studied for distributions which are s-ordered with respect to G. Some interval estimation problems for the unknown parameters of the k populations are studied. The infimum of the probability that a given confidence interval based on suitably chosen order statistics contains at least one good population is obtained. Different modifications and variations of this problem are also studied. The selection procedures are discussed in terms of majorization and weak majorization. The parameter is partially ordered by means of majorization or weak majorization. A class of procedures R sub h for selecting the best population is defined.
- Statistics and Probability