Optimal designs for homoscedastic functional polynomial measurement error models

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.