Orthogonality and D-optimality of the U-type design under general Fourier regression models

摘要

Riccomagno, Schwabe and Wynn (1997) gave a comprehensive study on D-optimality under a symmetric Fourier regression model and gave a characterization on orthogonality, complete orthogonality and Doptimality of lattice designs under a symmctrical Fourier model. This paper extends their results to asymmetric Fourier regression models. We give some necessary condition for the orthogonality and complete orthogonality of U-type designs under general Fourier regression models that involve symmetrical and asymmetrical Fourier models and prove that a U-type design, which is completely orthogonal, is not D-optimal for an asymmetrical Fourier model.