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D-optimal designs for full and reduced Fourier regression models

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  • Xiaojian Xu

    (Brock University)

  • Xiaoli Shang

    (Brock University)

Abstract

The optimal designs for Fourier regression models under the D-optimality criterion are discussed in this article. First, we investigate the D-optimal designs for estimating two coefficients corresponding to either sine or cosine terms in a full Fourier regression model. In many biological applications, estimating such specific pairs of coefficients is of interest. As a result of this article, the D-optimal designs for estimating these “coefficient pairs” can be constructed either explicitly or numerically for Fourier regression models with any order. Our resulting designs are provided for Fourier regression models with order less than 6. Secondly, we discuss the sensitivity of our resulting optimal designs for a full Fourier regression model when the true model is actually a reduced version of the assumed one. Lastly, we provide the algorithm for obtaining the D-optimal designs for a reduced Fourier regression model and the D-optimal designs for a useful reduced Fourier model are constructed. The comparison study shows that the constructed designs incorporating the reduced model are efficient.

Suggested Citation

  • Xiaojian Xu & Xiaoli Shang, 2017. "D-optimal designs for full and reduced Fourier regression models," Statistical Papers, Springer, vol. 58(3), pages 811-829, September.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:3:d:10.1007_s00362-015-0727-6
    DOI: 10.1007/s00362-015-0727-6
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    References listed on IDEAS

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    1. Holger Dette & Viatcheslav Melas & Andrey Pepelyshev, 2002. "D-Optimal Designs for Trigonometric Regression Models on a Partial Circle," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(4), pages 945-959, December.
    2. Holger Dette & Viatcheslav Melas & Piter Shpilev, 2007. "Optimal designs for estimating the coefficients of the lower frequencies in trigonometric regression models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(4), pages 655-673, December.
    3. Wiens, Douglas P., 1991. "Designs for approximately linear regression: two optimality properties of uniform designs," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 217-221, September.
    4. Xiaojian Xu & Xiaoli Shang, 2014. "Optimal and robust designs for trigonometric regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(6), pages 753-769, August.
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    Cited by:

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