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.

本文考虑了同调泛函多项式测量误差模型的最优设计。根据局部和贝叶斯D最优准则，给出了一般的等价定理，以检查给定设计的最优性。提供了局部和贝叶斯D最优设计的显式表征。通过对二次多项式测量误差模型的数值分析来说明结果。数值结果表明，误差方差比和模型参数是两种最优设计的重要因素。此外，还表明，如果错误方差比或模型参数指定不正确，贝叶斯D最优设计与局部D最优设计相比将更加健壮和有效。