CONTRIBUTIONS TO MULTIPLE DECISION THEORY
Abstract
The main contribution of this thesis is to propose and study new subset selection procedures for some important and interesting problems. Chapter I deals with Bayes and empirical Bayes rules for selecting good populations. Bayes procedures are derived for cases in which the conjugate prior distribution are gamma, beta, and normal distributions, respectively. In the unknown prior distribution case, we assume that the conditional distribution is uniform. Empirical Bayes procedures are also obtained for the case in which we are interested in comparing new treatments with a control--the control parameter may be known or unknown. Also the rate of convergence of such procedures is studied. Chapter II deals with nonparametric subset selection procedures for two-way layout in the analysis of variance. The proposed procedures are based on the Hodges-Lehmann estimators. It is shown that the proposed procedures have high efficiency. Also the problem of "Elimination of Strictly Non-t-Best" populations is studied in this chapter and some new results are obtained. Chapter III deals with optimality properties of some subset selection procedures. It should be pointed out that the formulation of the problem is more general than that in the earlier literature. First, we generalize the problem of Gupta and Huang (1980) to the unequal sample sizes case. Next, we treat a selection procedure as a multiple test. Based on this approach, we derive some optimality results. Finally, a problem very similar to that of Lehmann (1961) is considered for which results are derived using a different approach. Chapter IV deals with the problem of isotonic selection procedures. In this chapter we assume that the populations follow two-parameter exponential distributions. The location parameter (guarantee time) is the parameter of interest. It is assumed that the parameters of the treatment populations have an ascending ordering prior. Three isotonic procedures are proposed in this chapter. It is shown that the isotonic procedure is better than the classical procedure. Tables of associated constants for the proposed procedures are given in this chapter.
Degree
Ph.D.
Subject Area
Statistics
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.