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 max imizes the minimum of the D e ciency in the model of degree m and the D e ciencies in the models of degree m j m k j k given The resulting designs allow an e cient estimation of the parameters in the chosen regression and have reasonable e ciencies for checking the goodness of t of the assumed model of degree m by testing the highest coe cients 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 AMS Subject Classi cation K C