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Efficient design of experiment for exponential regression models

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  • Dette, Holger
  • Martinez Lopez, Ignacio
  • Ortiz Rodriguez, Isabel M.
  • Pepelyshev, Andrey

Abstract

In this paper robust and efficient designs are derived for several exponential decay models. These models are widely used in chemistry, pharmacokinetics or microbiology. We propose a maximin approach, which determines the optimal design such that a minimum of the D-efficiencies (taken over a certain range for the nonlinear parameters) becomes maximal. Analytic solutions are derived if optimization is performed in the class of minimal supported designs. In general the optimal designs with respect to the maximin criterion have to be determined numerically and some properties of these designs are also studied.

Suggested Citation

  • Dette, Holger & Martinez Lopez, Ignacio & Ortiz Rodriguez, Isabel M. & Pepelyshev, Andrey, 2004. "Efficient design of experiment for exponential regression models," Technical Reports 2004,08, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200408
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    References listed on IDEAS

    as
    1. Holger Dette, 1997. "Designing Experiments with Respect to ‘Standardized’ Optimality Criteria," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 97-110.
    2. Dette, Holger & Melas, Viatcheslav B. & Pepelyshev, Andrey, 2003. "Locally E-optimal designs for exponential regression models," Technical Reports 2003,37, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Dette, Holger & Haines, Linda M. & Imhof, Lorens A., 2003. "Maximin and Bayesian optimal designs for regression models," Technical Reports 2003,10, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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