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R-optimal designs for trigonometric regression models

Author

Listed:
  • Lei He

    (Shanghai Normal University)

  • Rong-Xian Yue

    (Shanghai Normal University
    Scientific Computing Key Laboratory of Shanghai Universities)

Abstract

This paper is concerned with the problem of constructing R-optimal designs for trigonometric regression models with different orders. More precisely, explicit R-optimal designs for the first-order trigonometric regression model on a partial cycle are derived by using the idea of complete class approach. The relative R-efficiency of the equidistant sampling method is then discussed. Moreover, when the explanatory variable varies in a complete cycle, the R-optimal designs for estimating the specific pairs of the coefficients in the trigonometric regression of larger order are obtained by invoking the equivalence theorem. Several examples are presented for illustration.

Suggested Citation

  • Lei He & Rong-Xian Yue, 2020. "R-optimal designs for trigonometric regression models," Statistical Papers, Springer, vol. 61(5), pages 1997-2013, October.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:5:d:10.1007_s00362-018-1017-x
    DOI: 10.1007/s00362-018-1017-x
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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. Xin Liu & Rong-Xian Yue, 2013. "A note on $$R$$ -optimal designs for multiresponse models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(4), pages 483-493, May.
    3. Holger Dette, 1997. "Designing Experiments with Respect to ‘Standardized’ Optimality Criteria," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 97-110.
    4. Lei He & Rong-Xian Yue, 2017. "R-optimal designs for multi-factor models with heteroscedastic errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 717-732, November.
    5. 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.
    6. Cun-Hui Zhang & Stephanie S. Zhang, 2014. "Confidence intervals for low dimensional parameters in high dimensional linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 217-242, January.
    7. 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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