Optimum partition procedures for separating good and bad treatments
成果类型：
Article
署名作者：
Giani, G; Strassburger, K
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.2307/2291473
发表日期：
1997
页码：
291-298
关键词：
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 nu degrees of freedom is (-1/nu)-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.