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Exact $$D$$ -optimal designs for first-order trigonometric regression models on a partial circle

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  • Fu-Chuen Chang
  • Lorens Imhof
  • Yi-Ying Sun

Abstract

Recently, various approximate design problems for low-degree trigonometric regression models on a partial circle have been solved. In this paper we consider approximate and exact optimal design problems for first-order trigonometric regression models without intercept on a partial circle. We investigate the intricate geometry of the non-convex exact trigonometric moment set and provide characterizations of its boundary. Building on these results we obtain a solution of the exact $$D$$ -optimal design problem. It is shown that the structure of the optimal designs depends on both the length of the design interval and the number of observations. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Fu-Chuen Chang & Lorens Imhof & Yi-Ying Sun, 2013. "Exact $$D$$ -optimal designs for first-order trigonometric regression models on a partial circle," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(6), pages 857-872, August.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:6:p:857-872
    DOI: 10.1007/s00184-012-0420-x
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Morales Martínez, Jorge Luis & Segovia-Domínguez, Ignacio & Rodríguez, Israel Quiros & Horta-Rangel, Francisco Antonio & Sosa-Gómez, Guillermo, 2021. "A modified Multifractal Detrended Fluctuation Analysis (MFDFA) approach for multifractal analysis of precipitation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    2. 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.

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