D-optimal designs for nonlinear models possessing a Chebyshev property

The paper is devoted to experimental design for nonlinear regression models, whose derivatives with respect to parameters generate a generalized Cheby-shev system. Most models of practical importance possess this property. In particular it is seen in exponential, rational and logistic models as well as splines with free knots. It is proved that support points of saturated locally D-optimal designs are monotonic and real analytic functions of initial values for those parameters on which models depend nonlinearly. This allows one to represent the functions by Taylor series. Similar properties of saturated maximin efficient designs are also investigated.