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Robust designs for polynomial regression by maximizing a minimum of D- and D1-efficiencies

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  • Dette, Holger
  • Franke, Tobias

Abstract

In the common polynomial regression of degree m we determine the design which maximizes the minimum of the D-efficiency in the model of degree m and the D-efficiencies in the models of degree m – j,…, m + k (j, k > 0 given). The resulting designs allow an efficient estimation of the parameters in the chosen regression and have reasonable efficiencies for checking the goodness-of-fit of the assumed model of degree m by testing the highest coefficients in the polynomials of degree m – j, … ; m + k. Our approach is based on a combination of the theory of canonical moments and general equivalence theory for minimax optimality criteria. The optimal designs can be explicitly characterized by evaluating certain associated orthogonal polynomials.

Suggested Citation

  • Dette, Holger & Franke, Tobias, 2000. "Robust designs for polynomial regression by maximizing a minimum of D- and D1-efficiencies," Technical Reports 2000,38, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200038
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    References listed on IDEAS

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    1. Wong, Weng Kee, 1994. "Comparing robust properties of A, D, E and G-optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 18(4), pages 441-448, November.
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