Constrained D-and D 1 -optimal Designs for Polynomial Regression
نویسندگان
چکیده
In the common polynomial regression model of degree m we consider the problem of determining the D-and D 1-optimal designs subject to certain constraints for the D 1-eeciencies 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 the question of the existence of a design satisfying all constraints. Our approach is based on a combination of general equivalence theory with the theory of canonical moments. In the case of equal bounds for the D 1-eeciencies the constrained optimal designs can be found explicitly by an application of recent results for associated orthogonal polynomials.
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