On a mixture of the D- and D1-optimality criterion in polynomial regression

Abstract

We consider a mixture of the D1-optimality criterion (minimizing the variance of the estimate for the highest coefficient) and the D-optimality criterion (minimizing the volume of the ellipsoid of concentration for the unknown parameter vector) in the polynomial regression model of degree n ⊆ N. The mixture is defined as a weighted product of both optimality criteria and explicit solutions are given for the proposed criterion. The derived designs have excellent efficiencies compared to the G-, D-, and D1-optimal design. This is illustrated in some examples for polynomial regression of lower degree. The optimal designs are calculated using the theory of canonical moments. Further applications are given in the field of model robust designs for polynomial regression models where only an upper bound for the degree of the polynomial regression model is known by the experimenter before the experiments are carried out.