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Constrained D- and D1-optimal designs for polynomial regression

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  • Dette, Holger
  • Franke, Tobias

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.

Suggested Citation

  • Dette, Holger & Franke, Tobias, 2000. "Constrained D- and D1-optimal designs for polynomial regression," Technical Reports 2000,37, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200037
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    Citations

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    Cited by:

    1. Montepiedra, Grace & Yeh, A.B.Arthur B., 2004. "Two-stage designs for identification and estimation of polynomial models," Computational Statistics & Data Analysis, Elsevier, vol. 46(3), pages 531-546, June.
    2. Min-Hsiao Tsai, 2012. "Efficient discriminating design for a class of nested polynomial regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(6), pages 809-817, August.
    3. McGree, J.M., 2017. "Developments of the total entropy utility function for the dual purpose of model discrimination and parameter estimation in Bayesian design," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 207-225.

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