© 2004 by Biometrika Trust
A comparison of sequential and non-sequential designs for discrimination between nested regression models
1 Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany holger.dette{at}ruhr-uni-bochum.de 2 RWTH Aachen, Institut für Medizinische Statistik, Pauwelstrasse 30, 52074 Aachen, Germany rkwiecien{at}medfak.rwth-aachen.de
Classical regression analysis is usually performed in two steps. In a first step an appropriate model is identified to describe the data-generating process and in a second step statistical inference is performed in the identified model.In this paper we investigate a sequential and a non-sequential design strategy, which take into account these different goals of the analysis for a class of nested models. It is demonstrated that non-sequential designs usually identify the ‘correct’ model with a higher probability than sequential methods. Although non-sequential designs can never be guaranteed to achieve the best possible efficiency in the ‘correct’ model, it is demonstrated by means of a simulation study that for realistic sample sizes the efficiencies of the non-sequential designs for the estimation of the parameters in the ‘correct’ model are at least as high as the corresponding efficiencies of the sequential methods.
Key Words: Discrimination design; F-test; Optimal design; Polynomial regression; Robust design; Sequential design
Received July 2002. Revised July 2003