On the functional approach to optimal designs for nonlinear models

This paper concerns locally optimal experimental designs for nonlinear regression models. It is based on the functional approach introduced in (Ser. Statist. 9 (1978) 45). In this approach, locally optimal design points and weights are studied as implicitly given functions of the nonlinear parameters included in the model. Representing these functions in a Taylor series enables an analytical solution of the optimal design problem for many nonlinear models. A wide class of such models is introduced here. It includes, in particular, three parameters logistic distribution, hyperexponential and rational models. For these models we construct the analytical solution and use it for studying the efficiency of locally optimal designs. As a criterion of optimality the well-known D-criterion is considered.