Optimal designs for a class of nonlinear regression models

For a broad class of nonlinear regression models we investigate the local E- and c-optimal design problem. It is demonstrated that in many cases the optimal designs with respect to these optimality criteria are supported at the Chebyshev points, which are the local extrerna of the equi-oscillating best approximation of the function f(0) equivalent to 0 by a normalized linear combination of the regression functions in the corresponding linearized model. The class of models includes rational, logistic and exponential models and for the rational regression models the E- and c-optimal design problem is solved explicitly in many cases.