T-optimal designs for discrimination between rational and polynomial models

Abstract

This paper considers the problem of the analytical construction of experimental designs optimal with respect to the popular T-optimality criterion proposed by A.C. Atkinson and V.V. Fedorov in 1975 for discrimination between the simplest rational and polynomial regression models. It is shown how the classical results from approximation theory can be used to derive explicit formulas describing the behavior of support points and weights of T-optimal designs for different fixed parameter values. An applied discrimination problem for rational and polynomial regression models is considered as an example. For this models the numerical construction of experimental designs optimal with respect to robust analogues of T-criterion is also briefly discussed.