Some Results in the Theory of Subset Selection Procedures.

Abstract : Selection and ranking (ordering) problems in statistical inference arise mainly because the classical tests of homogeneity are often inadequate in certain situations where the experimenter is interested in comparing k ( or = 2) populations, treatments or processes with the goal of selecting one or more worth-while (good) population. Chapter I of this thesis considers the problem of selecting a subset containing all populations that are better than a control under the assumptions of an ordering prior. Here, by an ordering prior we mean that there exists a known simple or partial order relationship among the unknown parameters of the treatments (excluding the control). Three new selection procedures are proposed and studied. These procedures do meet the usual requirement that the probability of a correct selection is greater than or equal to a pre-determined number P*. Two of the three procedures use the isotonic regression over the sample means of the k treatments with respect to the given ordering prior. Tables which are necessary to carry out the selection procedure with isotonic approach for the selection of unknown means of normal populations and gamma populations are given. Monte Carlo comparisons on the performance of several procedures for the normal or gamma means problem were carried out in several selected cases. The results of this study seem to indicate that the procedures based on isotonic estimators always have superior prformance, especially, when there are more than one bad population (in comparison with the control).