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A p-step-ahead sequential adaptive algorithm for D-optimal nonlinear regression design

Author

Listed:
  • Fritjof Freise

    (University of Veterinary Medicine Hannover)

  • Norbert Gaffke

    (University of Magdeburg)

  • Rainer Schwabe

    (University of Magdeburg)

Abstract

Under a nonlinear regression model with univariate response an algorithm for the generation of sequential adaptive designs is studied. At each stage, the current design is augmented by adding p design points where p is the dimension of the parameter of the model. The augmenting p points are such that, at the current parameter estimate, they constitute the locally D-optimal design within the set of all saturated designs. Two relevant subclasses of nonlinear regression models are focused on, which were considered in previous work of the authors on the adaptive Wynn algorithm: firstly, regression models satisfying the ‘saturated identifiability condition’ and, secondly, generalized linear models. Adaptive least squares estimators and adaptive maximum likelihood estimators in the algorithm are shown to be strongly consistent and asymptotically normal, under appropriate assumptions. For both model classes, if a condition of ‘saturated D-optimality’ is satisfied, the almost sure asymptotic D-optimality of the generated design sequence is implied by the strong consistency of the adaptive estimators employed by the algorithm. The condition states that there is a saturated design which is locally D-optimal at the true parameter point (in the class of all designs).

Suggested Citation

  • Fritjof Freise & Norbert Gaffke & Rainer Schwabe, 2024. "A p-step-ahead sequential adaptive algorithm for D-optimal nonlinear regression design," Statistical Papers, Springer, vol. 65(5), pages 2811-2834, July.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:5:d:10.1007_s00362-023-01502-4
    DOI: 10.1007/s00362-023-01502-4
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    References listed on IDEAS

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    1. Luc Pronzato, 2010. "One-step ahead adaptive D-optimal design on a finite design space is asymptotically optimal," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(2), pages 219-238, March.
    2. Biedermann, Stefanie & Dette, Holger & Zhu, Wei, 2006. "Optimal Designs for DoseResponse Models With Restricted Design Spaces," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 747-759, June.
    3. Fritjof Freise & Norbert Gaffke & Rainer Schwabe, 2021. "Convergence of least squares estimators in the adaptive Wynn algorithm for some classes of nonlinear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(6), pages 851-874, August.
    Full references (including those not matched with items on IDEAS)

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