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Optimal design for additive partially nonlinear models

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  • S. Biedermann
  • H. Dette
  • D. C. Woods

Abstract

We develop optimal design theory for additive partially nonlinear regression models, showing that Bayesian and standardized maximin D-optimal designs can be found as the products of the corresponding optimal designs in one dimension. A sufficient condition under which analogous results hold for D s -optimality is derived to accommodate situations in which only a subset of the model parameters is of interest. To facilitate prediction of the response at unobserved locations, we prove similar results for Q-optimality in the class of all product designs. The usefulness of this approach is demonstrated through an application from the automotive industry, where optimal designs for least squares regression splines are determined and compared with designs commonly used in practice. Copyright 2011, Oxford University Press.

Suggested Citation

  • S. Biedermann & H. Dette & D. C. Woods, 2011. "Optimal design for additive partially nonlinear models," Biometrika, Biometrika Trust, vol. 98(2), pages 449-458.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:2:p:449-458
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    File URL: http://hdl.handle.net/10.1093/biomet/asr001
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    Citations

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    Cited by:

    1. Lei He, 2021. "Bayesian optimal designs for multi-factor nonlinear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 223-233, March.
    2. Lei He & Rong-Xian Yue, 2017. "R-optimal designs for multi-factor models with heteroscedastic errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 717-732, November.
    3. Rui Li & Yuanyuan Zhang, 2021. "Two-stage estimation and simultaneous confidence band in partially nonlinear additive model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1109-1140, November.
    4. He, Lei, 2018. "Optimal designs for multi-factor nonlinear models based on the second-order least squares estimator," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 201-208.
    5. Thomas Schaubroeck & Simon Schaubroeck & Reinout Heijungs & Alessandra Zamagni & Miguel Brandão & Enrico Benetto, 2021. "Attributional & Consequential Life Cycle Assessment: Definitions, Conceptual Characteristics and Modelling Restrictions," Sustainability, MDPI, vol. 13(13), pages 1-47, July.

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