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

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  • Xie, Min-Yu
  • Ning, Jian-Hui
  • Fang, Kai-Tai

Abstract

Riccomagno et al. [1997. Lattice-based D-optimum design for Fourier regression. Ann. Statist. 25, 2313-2317] gave a comprehensive study on D-optimality under a symmetric Fourier regression model and gave a characterization on orthogonality, complete orthogonality and D-optimality of lattice designs under a symmetrical 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.

Suggested Citation

  • Xie, Min-Yu & Ning, Jian-Hui & Fang, Kai-Tai, 2007. "Orthogonality and D-optimality of the U-type design under general Fourier regression models," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1377-1384, July.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:12:p:1377-1384
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    Cited by:

    1. Lin Wang & Hongquan Xu & Min-Qian Liu, 2023. "Fractional factorial designs for Fourier-cosine models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(3), pages 373-390, April.

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