Optimal multipurpose designs for regression models

Abstract

In this paper multipurpose designs are considered. Therefore the criterion

is used to choose a design, where M_m(ξ) are the information matrices of a design ξ for several models. With suitable chosen matrices A_mj, a S-optimal design is good for the estimation of parameters in several models at the same time or for the discrimination between two models together with the estimation in the accepted model. Results of A. C. ATKINSON and S. M. STIGLER generalized in this way. For S-optimal designs among others an Equivalence Theorem of the KIEFER-WOLFOWITZ typ is proved and computing methods are given. It should be noticed that the regularity of the information matrices is not used.