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Optimal designs for homoscedastic functional polynomial measurement error models

Author

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  • Min-Jue Zhang

    (Shanghai Normal University
    Chizhou University)

  • Rong-Xian Yue

    (Shanghai Normal University)

Abstract

This paper considers the construction of optimal designs for homoscedastic functional polynomial measurement error models. The general equivalence theorems are given to check the optimality of a given design, based on the locally and Bayesian D-optimality criteria. The explicit characterizations of the locally and Bayesian D-optimal designs are provided. The results are illustrated by numerical analysis for a quadratic polynomial measurement error model. Numerical results show that the error-variances ratio and the model parameter are the important factors for the both optimal designs. Moreover, it is shown that the Bayesian D-optimal design is more robust and effective compared with the locally D-optimal design, if the error-variances ratio or the model parameter is misspecified.

Suggested Citation

  • Min-Jue Zhang & Rong-Xian Yue, 2021. "Optimal designs for homoscedastic functional polynomial measurement error models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 485-501, September.
    • Handle: RePEc:spr:alstar:v:105:y:2021:i:3:d:10.1007_s10182-021-00399-4
    DOI: 10.1007/s10182-021-00399-4
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    References listed on IDEAS

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    1. M. Konstantinou & H. Dette, 2015. "Locally optimal designs for errors-in-variables models," Biometrika, Biometrika Trust, vol. 102(4), pages 951-958.
    2. Min-Jue Zhang & Rong-Xian Yue, 2020. "Locally D-optimal designs for heteroscedastic polynomial measurement error models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 643-656, August.
    3. Dette, Holger & Bretz, Frank & Pepelyshev, Andrey & Pinheiro, José, 2008. "Optimal Designs for Dose-Finding Studies," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1225-1237.
    4. Maria Konstantinou & Holger Dette, 2017. "Bayesian D‐optimal designs for error‐in‐variables models," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(3), pages 269-281, May.
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