The partitioning principle: A powerful tool in multiple decision theory

• 成果类型: Article
• 署名作者: Finner, H; Strassburger, K
• 署名单位: Heinrich Heine University Dusseldorf
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2002
• 页码: 1194-1213
• 关键词: stepwise; ADVANTAGES

摘要

A first general principle and nowadays state of the art for the construction of powerful multiple test procedure, controlling a multiple level alpha is the so-called closure principle. In this article we introduce another powerful tool for the construction of multiple decision procedures. especially for the construction of multiple test procedure, and,election procedure. This tool is based on a partition of the parameter space and will be called partitioning principle (PP). In the first part of the paper we review basic concepts of multiple hypotheses testing and discuss a slight generalization of the Current theory. In the second part we present various variants of the PP for the construction of multiple test procedures. these are a general PP (GPP), a weak PP (WPP) and a strong PP (SPP). It will be shown that, depending on the underlying decision problem, a PP may lead to more powerful test procedures than a formal application of the closure principle (FCP). Moreover. the more complex SPP may be more powerful than the WPP. Based on a duality between testing and selecting PPs can also be applied for the construction of more powerful selection procedures. In the third part of the paper FCP, WPP and SPP are applied and compared in some examples.