D-optimal designs for weighted polynomial regression

By utilizing the equivalence theorem and Descartes's rule of signs, we construct D-optimal designs for a weighted polynomial regression model of degree k, with specific weight function w(x)=1/(a2-x2)[delta], on the compact interval [-1,1]. The main result shows that in most cases, the number of support points of the D-optimal design is k+1, while in other cases, the D-optimal design has k+2 support points.Approximate design Descartes's rule of signs Equivalence theorem Weighted polynomial regression