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T-optimal discriminating designs for Fourier regression models

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  • Dette, Holger
  • Melas, Viatcheslav B.
  • Shpilev, Petr

Abstract

The problem of constructing T-optimal discriminating designs for Fourier regression models is considered. Explicit solutions of the optimal design problem for discriminating between two Fourier regression models, which differ by at most three trigonometric functions, are provided. In general, the T-optimal discriminating design depends in a complicated way on the parameters of the larger model, and for special configurations of the parameters T-optimal discriminating designs can be found analytically. Moreover, in the remaining cases this dependence is studied by calculating the optimal designs numerically. In particular, it is demonstrated that D- and Ds-optimal designs have rather low efficiencies with respect to the T-optimality criterion.

Suggested Citation

  • Dette, Holger & Melas, Viatcheslav B. & Shpilev, Petr, 2017. "T-optimal discriminating designs for Fourier regression models," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 196-206.
    • Handle: RePEc:eee:csdana:v:113:y:2017:i:c:p:196-206
    DOI: 10.1016/j.csda.2016.06.010
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    References listed on IDEAS

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    1. Wiens, Douglas P., 2010. "Robustness of design for the testing of lack of fit and for estimation in binary response models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3371-3378, December.
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    4. Shih-Kang Chao & Katharina Proksch & Holger Dette & Wolfgang Karl Härdle, 2017. "Confidence Corridors for Multivariate Generalized Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 70-85, January.
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    6. Stefanie Biedermann & Holger Dette & Philipp Hoffmann, 2009. "Constrained optimal discrimination designs for Fourier regression models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 143-157, March.
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