Optimal designs for trigonometric regression models

In the common Fourier regression model we investigate the optimal design problem for the estimation of linear combinations of the coefficients, where the explanatory variable varies in the interval [−pi, pi]. In a recent paper Dette et. al. (2008) determined optimal designs for estimating certain pairs of the coefficients in the model. The optimal design problem corresponds to a linear optimality criterion for a specific matrix L. In the present paper these results are extended to more general matrices L. By our results the optimal design problem for a Fourier regression of large degree can be reduced to a design problem in a model of lower degree, which allows the determination of L-optimal designs in many important cases. The results are illustrated by several examples