On a functional approach to locally optimal designs

This paper concerns locally optimal experimental designs for nonlinear regression models. It is based on the functional approach introduced in Melas (1978). 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 analytical solution of the optimal design problem for many nonlinear models. A wide class of such models is here introduced. It includes, in particular, the three-parameter logistic model. For this model we construct the analytical solution and use it for studying the efficiency of locally optimal designs. As a criterion of optimahty the well known D-criterion is considered.