Locally D -optimal designs for a class of generalized functional measurement error models

This paper investigates the optimal design problem for a class of generalized functional measurement error models, in which some covariates contain measurement errors. Utilizing the locally D-optimality criterion, an equivalence theorem is established to verify the optimality of a given design. Furthermore, it is demonstrated that local D-optimal designs for such models can be derived explicitly. Specifically, under certain sufficient conditions, the locally D-optimal design for the generalized functional measurement error model can be expressed as the product of the designs for the corresponding measurement error model and the classical regression model. Two examples are provided to illustrate these theoretical results.