Optimal designs for estimating the slope in nonlinear regression

Abstract

We consider the problem of estimating the slope of the expected response in nonlinear regression models. It is demonstrated that in many cases the optimal designs for estimating the slope are either on k or k - 1 points, where k denotes a number of unknown parameters in the model. It is also shown that the support points and weights of the optimal designs are analytic functions, and this result is used to construct a numerical procedure for the calculation of the optimal designs. The results are illustrated in exponential regression and rational regression models.