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Maximin and Bayesian optimal designs for regression models

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  • Dette, Holger
  • Haines, Linda M.
  • Imhof, Lorens A.

Abstract

For many problems of statistical inference in regression modelling, the Fisher information matrix depends on certain nuisance parameters which are unknown and which enter the model nonlinearly. A common strategy to deal with this problem within the context of design is to construct maximin optimal designs as those designs which maximize the minimum value of a real valued (standardized) function of the Fisher information matrix, where the minimum is taken over a specified range of the unknown parameters. The maximin criterion is not differentiable and the construction of the associated optimal designs is therefore difficult to achieve in practice. In the present paper the relationship between maximin optimal designs and a class of Bayesian optimal designs for which the associated criteria are differentiable is explored. In particular, a general methodology for determining maximin optimal designs is introduced based on the fact that in many cases these designs can be obtained as weak limits of appropriate Bayesian optimal designs.

Suggested Citation

  • 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.
    • Handle: RePEc:zbw:sfb475:200310
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    References listed on IDEAS

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    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.
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    1. Dette, Holger & Haines, Linda M. & Imhof, Lorens A., 2003. "Bayesian and maximin optimal designs for heteroscedastic regression models," Technical Reports 2003,36, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Dette, Holger & Melas, Viatcheslav B. & Strigul, Nikolay, 2003. "Design of experiments for microbiological models," Technical Reports 2003,41, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. 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.
    4. Pepelyshev, Andrey & Melas, Viatcheslav B. & Strigul, Nikolay & Dette, Holger, 2004. "Design of experiments for the Monod model : robust and efficient designs," Technical Reports 2004,36, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    5. Biedermann, Stefanie & Dette, Holger & Pepelyshev, Andrey, 2003. "Maximin optimal designs for the compartmental model," Technical Reports 2003,35, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    6. Dette, Holger & Biedermann, Stefanie & Pepelyshev, Andrey, 2004. "Some robust design strategies for percentile estimation in binary response models," Technical Reports 2004,19, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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