R-optimal designs for trigonometric regression models

This paper is concerned with the problem of constructing R-optimal designs for trigonometric regression models with different orders. More precisely, explicit R-optimal designs for the first-order trigonometric regression model on a partial cycle are derived by using the idea of complete class approach. The relative R-efficiency of the equidistant sampling method is then discussed. Moreover, when the explanatory variable varies in a complete cycle, the R-optimal designs for estimating the specific pairs of the coefficients in the trigonometric regression of larger order are obtained by invoking the equivalence theorem. Several examples are presented for illustration.