Optimum Partition Procedures for Separating Good and Bad Treatments

原文摘要

This article considers partitioning a given set of competing treatments into two subsets with the purpose of separating good and bad treatments. (The qualities “good” and “bad” are defined in terms of the parameter vector of the underlying distribution family.) Regarding the probability of an incorrect partition, within the class of so-called natural procedures minimax solutions are derived under suitable distributional assumptions. These results extend previous investigations to the larger family of quasi-concave distributions. It is shown that the multivariate noncentral t distribution with v degrees of freedom is (-1/v)-concave, and hence quasi-concave. Thus the unknown variance case in a normal distribution setup is covered as a special application. Specifically, for partitioning with respect to a control, the presented minimax results are used in the unknown variance case to determine optimal allocations of total sample sizes that guarantee a correct partition at a preassigned confidence level. Optimum procedures for partitioning linear contrasts in the normal case are also discussed.

摘要来源：OpenAlex 索引摘要（稿件版本未注明）