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Optimal and robust designs for trigonometric regression models

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  • Xiaojian Xu
  • Xiaoli Shang

Abstract

This article presents discussions on the optimal and robust designs for trigonometric regression models under different optimality criteria. First, we investigate the classical Q-optimal designs for estimating the response function in a full trigonometric regression model with a given order. The equivalencies of Q-, A-, and G-optimal designs for trigonometric regression in general are also articulated. Second, we study minimax designs and their implementation in the case of trigonometric approximation under Q-, A-, and D-optimality. Then, We indicate the existence of the symmetric designs that are D-optimal minimax designs for general trigonometric regression models, and prove the existence of the symmetric designs that are Q- or A-optimal minimax designs for two particular trigonometric regression models under certain conditions. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • 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.
    • Handle: RePEc:spr:metrik:v:77:y:2014:i:6:p:753-769
    DOI: 10.1007/s00184-013-0463-7
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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. 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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    Cited by:

    1. Lucy L. Gao & Julie Zhou, 2017. "D-optimal designs based on the second-order least squares estimator," Statistical Papers, Springer, vol. 58(1), pages 77-94, March.
    2. 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.
    3. Lei He & Rong-Xian Yue, 2020. "R-optimal designs for trigonometric regression models," Statistical Papers, Springer, vol. 61(5), pages 1997-2013, October.

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