Some contributions to the theory and applications of nonparametric subset selection procedures

Abstract

Choosing the best population (based on some parameter performance) among alternative populations can be challenging. The decision-making process depends on what factors are considered important by the person making the decision. On order to determine which populations are better among k of them, an experiment should be designed, and samples from each population are to be taken and the sample size needs to be determined. The target here is not to estimate any unknown parameter, but rather to select the population with the best parameter value. The methodological topic of this dissertation is the nonparametric approach to subset selection of populations so as to contain the “best” population -to be defined with a user-prescribed probability of a correct selection, where we will examine how to apply a versatile, nonparametric framework to efficiently and accurately choose subsets of populations while ensuring that users can control the reliability of the selections made. The common approach in this problem context has been to rank the data (as it is a well established approach) and base the statistical inference on population rank sums. The process of ranking and calculating rank sums is relatively straightforward, facilitating easier interpretation of results and it can be adapted to different contexts and objectives, whether for hypothesis testing or selecting the best population, enabling researchers to base their choices on relative performance as opposed to absolute measurements. In this dissertation, alternative rank scoring methods are considered and shown, in some cases, to yield smaller selected subsets with the same assurance probability as with rank sums. The investigations herein considered are for a two-way experimental block design. An application of the research developed here is made to state motor vehicle traffic fatality rates for the years 1994–2022 with the goal of selecting a subset of states to contain the best (worst) with a prescribed probability. The effects of alternate scoring rules are displayed and shown to support a practical conclusion for other applications.