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.
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Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grants (11971318, 11871143), Shanghai Rising-Star Program (No. 20QA1407500) and the Natural Science Foundation of Shanghai (No. 19ZR1437000).
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Zhang, MJ., Yue, RX. Optimal designs for homoscedastic functional polynomial measurement error models. AStA Adv Stat Anal 105, 485–501 (2021). https://doi.org/10.1007/s10182-021-00399-4
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DOI: https://doi.org/10.1007/s10182-021-00399-4