T-optimal discriminating designs for Fourier regression models

The problem of constructing T-optimal discriminating designs for Fourier regression models is considered. Explicit solutions of the optimal design problem for discriminating between two Fourier regression models, which differ by at most three trigonometric functions, are provided. In general, the T-optimal discriminating design depends in a complicated way on the parameters of the larger model, and for special configurations of the parameters T-optimal discriminating designs can be found analytically. Moreover, in the remaining cases this dependence is studied by calculating the optimal designs numerically. In particular, it is demonstrated that D- and Ds-optimal designs have rather low efficiencies with respect to the T-optimality criterion.