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Design of experiments with unknown parameters in variance

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  • Valerii V. Fedorov
  • Robert C. Gagnon
  • Sergei L. Leonov

Abstract

Model fitting when the variance function depends on unknown parameters is a popular problem in many areas of research. Iterated estimators which are asymptotically equivalent to maximum likelihood estimators are proposed and their convergence is discussed. From a computational point of view, these estimators are very close to the iteratively reweighted least‐squares methods. The additive structure of the corresponding information matrices allows us to apply convex design theory which leads to optimal design algorithms. We conclude with examples which illustrate how to bridge our general results with specific applied needs. In particular, a model with experimental costs is introduced and is studied within the normalized design paradigm. Copyright © 2002 John Wiley & Sons, Ltd.

Suggested Citation

  • Valerii V. Fedorov & Robert C. Gagnon & Sergei L. Leonov, 2002. "Design of experiments with unknown parameters in variance," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 18(3), pages 207-218, July.
    • Handle: RePEc:wly:apsmbi:v:18:y:2002:i:3:p:207-218
    DOI: 10.1002/asmb.474
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    Cited by:

    1. Idais, Osama, 2020. "Locally optimal designs for multivariate generalized linear models," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    2. Soumaya, Moudar & Gaffke, Norbert & Schwabe, Rainer, 2015. "Optimal design for multivariate observations in seemingly unrelated linear models," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 48-56.
    3. Cong Han & Kathryn Chaloner, 2004. "Bayesian Experimental Design for Nonlinear Mixed-Effects Models with Application to HIV Dynamics," Biometrics, The International Biometric Society, vol. 60(1), pages 25-33, March.

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