Subset Selection: Robustness and Imprecise Selection

摘要

Assume k (integer k equal to or greater than 2) independent populations aregiven. The associated independent random variables have distributions with an unknown location parameter. The goal is to select the best population, this is the population with largest value of the location parameter. Some distributional and robustness results for subset selection from normal populations are reviewed. Special attention is given to the probability of correct selection. Some distributional results are given. Explicit expressions for expectation and variance of the subset size using subset selection are presented. Some remarks concerning a generalized selection goal using subset selection are made. Instead of selecting precisely the best population, an imprecise selection can be applied, that is selection of the population in the neighborhood of the best population. The generalized subset selection goal is to select a non-empty subset of populations that contains at least one almost best population with a certain confidence level. For a collection of populations with an unknown location parameter an almost best population, or more accurately an epsilon best population, is defined as a population with location parameter, a distance less than or equal to epsilon (with epsilon equal to or greater than 0) from the maximal value of the location parameter for all populations. The selection of an almost best population is compared with the selection of the best one from an application point of view. Some efficiency results are presented.