On δ-equivalence with the best in k-sample models

• 成果类型: Article
• 署名作者: Finner, H.; Strassburger, K.
• 署名单位: Heinrich Heine University Dusseldorf; Leibniz Association; Deutsches Diabetes-Zentrum (DDZ)
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214505000001014
• 发表日期: 2006
• 页码: 737-746
• 关键词: multiple-comparison procedures; confidence-intervals; range

摘要

In recent work we introduced a general, a weak, and a strong partitioning principles for the construction of multiple decision procedures as multiple testing or selection procedures. Partitioning principles can be viewed as natural extensions of the closure principle and sometimes yield more powerful decision procedures. In this article we consider the problem of establishing equivalence with the best with respect to k treatment means, where equivalence is defined in terms of a threshold value delta > 0. We reformulate the original selection problem as a multiple testing problem and develop various step-down and step-up procedures by applying the closure principle and partitioning principles. The new step-down procedure is shown to provide a uniform improvement over procedures currently in use. Moreover, we propose some projection methods that yield confidence intervals being compatible with stepwise tests and selection procedures.