Name: Finner

Firstname: Helmut

Title: Prof. Dr.

Institution: Deutsches Diabetes-Forschungsinstitut, Abteilung Biometrie und Epidemiologie

Street: Aufm Hennekamp

City: Duesseldorf

Zip-Code: 40225

Country: Germany

Phone: +49 02113382352

Fax: +49 02113382677

Email: finner@ddfi.uni-duesseldorf.de

Authors: Helmut Finner und Klaus Strassburger

Title: The partitioning principle: A powerful tool in multiple decision theory

Abstract: A first general principle and nowadays state of the art for the construction of powerful multiple test procedures controlling a multiple level $\alpha$ is the so-called closure principle. In this talk we introduce another powerful tool for the construction of multiple decision procedures, especially for the construction of multiple test procedures and selection procedures. This tool is based on a partition of the parameter space and will be called partitioning principle (PP). We discuss various variants of the PP, 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 PP`s can also be applied for the construction of more powerful selection procedures. FCP, WPP and SPP will be applied and compared in some examples.

References: Finner, H. and Strassburger, K. (2002). The partitioning principle: A powerful tool in multiple decision theory. The Annals of Statistics 30, to appear.