Constrained D - and D 1-optimal designs for polynomial regression

Abstract

In the common polynomial regression model of degree m we consider the problem of determining the D- and D1 -optimal designs subject to certain constraints for the D1 - efficiencies in the models of degree mIn the common polynomial regression model of degree m we consider the problem of determining the D- and D1-optimal designs subject to certain constraints for the D_1-efficiencies in the models of degree m - j;m - j + 1 ; : : : ;m+ k (m > j>=0; k>=0 given). We present a complete solution of these problems, which on the one hand allow a fast computation of the constrained optimal designs and on the other hand give an answer to on a combination of general equivalence theory with the theory of canonical moments. In the case of equal bounds for the D_1-effciencies the constrained optimal designs can be found explicitly by an application of recent results for associated orthogonal polynomials.