Statistica Sinica

Holger Dette and William J. Studden

Abstract:This paper considers the problem of determining efficient designs for polynomial regression models when only an upper bound for the degree of the polynomial is known by the experimenter before the experiments are carried out. The optimality criterion maximizes a weightedp-mean of the relativeD-efficiencies in the different models. The optimal (model robust) design is completely determined in terms of its canonical moments which form the unique solution of a system of nonlinear equations. The efficiency of the optimal designs with respect to different criteria is investigated by several examples.

Key words and phrases:Canonical moments, D-efficiency, equivalence theorem, mixture of optimality criteria, polynomial regression.