Constrained D- and D1-optimal designs for polynomial regression

Holger Dette and Tobias Franke

No 2000,37, Technical Reports from Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen

Abstract: In the common polynomial regression model of degree m we consider the problem of determining the D- and D1-optimal designs subject to certain constraints for the D- efficiencies in the models of degree m – j,m + j , … 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 D1-efficiencies the constrained optimal designs can be found explicitly by an application of recent results for associated orthogonal polynomials.

Keywords: Constrained optimal designs; polynomial regression; D- and D1-optimal designs; associated orthogonal polynomials (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (3)

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