Some Characteristics of a Ranking Procedure for Population Parameters Based on Chi-Square Statistics

Abstract

A recurring statistical problem is the cbmplete ordering of a set of k distributions (or populations) with respect to some parameter. A related problem is the selection of the largest or smallest parameter of k distributions. In this paper we examine the characteristics of an ad hoc procedure for populations which admit a x 2 statistic, as a function of an estimator for the population parameter, and use these statistics to order the populations. Lower bounds for the probability of correct, ranking, of selecting the smallest, and of selecting the largest parameter are provided as a function of degrees of freedom and the number of populations to be ordered, k, for k = 3(1)8