OPTIMAL DESIGNS FOR POLYNOMIAL REGRESSION WHEN THE DEGREE IS NOT KNOWN

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 weighted p-mean of the relative D-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.