Title: Prof. Dr.
Institution: Deutsches Diabetes-Forschungsinstitut, Abteilung Biometrie und Epidemiologie
Street: Aufm Hennekamp 65
Phone: +49 211 3382 258
Fax: +49 211 3382 677
Authors: G. Giani, H. Finner, K. Strassburger
Title: Subset Selection of Good Populations: Partitioning Principle, Power Control, and Software
Abstract: The general duality between multiple testing and selecting examined in Finner & Giani (1996) has led to a better understanding of the structure of many subset selection procedures proposed in the literature. Based on this duality, first improvements of existing selection procedures were obtained by mainly applying the well-known closure principle to their corresponding multiple testing problems. Recently Finner & Strassburger (2001) introduced a general partitioning principle as a natural extension of the closue principle, whose application to selection problems should let expect further significant improvements. In this contribution such improvements are explicitly established for the special problem of selecting all good populations. Here good and bad populations are defined in terms of their distances from the best. The primary task to make the critical values of the resulting new step-down selection procedures numerically calculable is to beforehand solve com! plex LFC-problems. Furthermore, contol of the power defined as probability of not selecting any of the bad populations is addressed. The problem of finding the least favorable power over all those parameter configurations with at least one bad population is a non-convex problem and thus a difficult task. To overcome the trouble in solving this problem, a lower bound is derived which turns out to be very close to the exact solution. For a one-way layout, minimum sample sizes controlling the power at some prespecified level are compared with those of various other well-known selection rules to demonstarte the superiority of the proposed procedure. In order to control a correct selection of all good populations with simultaneous exclusion of all the bad ones we finally discuss a single-step procedure. All the procedures dealt with are implemented in the software package SEPARATE which is briefly presented. SEPARATE can be downloaded from http://www.ddfi.uni-duesseldorf.de/main! /separate/index.htm.
References: Finner, H. & Giani, G. (1996): Duality between multiple testing and selecting. J. Statist. Planning Infer. 54, 201-227.
Finner, H. & Strassburger, K. (2001): The partitioning principle: A powerful tool in multiple decision theory. Ann Statist., in press.