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

Holger Dette and Tobias Franke

No 2000,38, Technical Reports from Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen

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.

Keywords: Minimax optimal designs; robust design; D-optimality; D1-optimality; t-test; associated orthogonal polynomials (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb475:200038

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