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A functional-algebraic determination of D-optimal designs for trigonometric regression models on a partial circle

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  • Dette, Holger
  • Melas, Viatcheslav B.
  • Biedermann, Stefanie

Abstract

We investigate the D-optimal design problem in the common trigonometric regression model, where the design space is a partial circle. The task of maximizing the criterion function is transformed into the problem of determining an eigenvalue of a certain matrix via a differential equation approach. Since this eigenvalue is an analytic function of the length of the design space, we can make use of a Taylor expansion to provide a recursive algorithm for its calculation. Finally, this enables us to determine Taylor expansions for the support points of the D-optimal design.

Suggested Citation

  • Dette, Holger & Melas, Viatcheslav B. & Biedermann, Stefanie, 2002. "A functional-algebraic determination of D-optimal designs for trigonometric regression models on a partial circle," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 389-397, July.
    • Handle: RePEc:eee:stapro:v:58:y:2002:i:4:p:389-397
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    1. Dette, Holger & Melas, Viatcheslav B. & Pepelyshev, Andrey, 2001. "D-optimal designs for trigonometric regression models on a partial circle," Technical Reports 2001,11, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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    Cited by:

    1. Fu-Chuen Chang, 2005. "D-Optimal designs for weighted polynomial regression—A functional approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(4), pages 833-844, December.
    2. Harman, Radoslav & Jurík, Tomás, 2008. "Computing c-optimal experimental designs using the simplex method of linear programming," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 247-254, December.
    3. Yue, Rong-Xian & Liu, Xin, 2010. "-optimal designs for a hierarchically ordered system of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3458-3465, December.
    4. 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.
    5. Alqallaf, Fatemah & Huda, S., 2013. "Minimax designs for the difference between two estimated responses in a trigonometric regression model," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 909-915.

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