Robust designs for polynomial regression by maximizing a minimum of D- and D1-efficiencies

In the common polynomial regression of degree m we determine the design which maximizes the minimum of the D-efficiency in the model of degree m and the D₁-efficiencies in the models of degree m-j,, m +k (j, k≥ 0 given). The resulting designs allow an efficient estimation of the parameters in the chosen regression and have reasonable efficiencies for checking the goodness-of-fit of the assumed model of degree m by testing the highest coefficients in the polynomials of degree m-j,, m +k . Our approach is based on a combination of the theory of canonical moments and general equivalence theory for minimax optimality criteria. The optimal designs can be explicitly characterized by evaluating certain associated orthogonal polynomials.