Abstract
Using an Equivalence Theorem and the theory of Sturm-Liouville systems, we determine the D-optimal designs for some classes of weighted polynomial regression of degree d on the interval [−1, 1]. We also show that the number of the optimal support points for such models is d + 1. and that the optimal support points can be computed through a specific eigenvalue of a certain band matrix. Some results of Karlin and Studden ( Ann. Math. Statist. 37 (1996), 783–815) turn out to be special cases of our results.
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