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/(a(2) - x(2))(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. (C) 2003 Elsevier Science B.V. All rights reserved.