Abstract: We consider the problem of finding an efficient design for estimating the model parameters and the mean response surface simultaneously when the true degree of the polynomial model is unknown. A precision constraint is imposed on one of these estimates and the optimal design is found using the theory of canonical moments. Robustness properties of the optimal designs to model assumptions and their performances relative to similar designs are studied.
Key words and phrases: Canonical moment, continuous design, D-optimality, G-optimality, robust design criteria.