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Constructing K-optimal designs for regression models

Author

Listed:
  • Zongzhi Yue

    (University of Victoria)

  • Xiaoqing Zhang

    (University of Victoria)

  • P. van den Driessche

    (University of Victoria)

  • Julie Zhou

    (University of Victoria)

Abstract

We study approximate K-optimal designs for various regression models by minimizing the condition number of the information matrix. This minimizes the error sensitivity in the computation of the least squares estimator of regression parameters and also avoids the multicollinearity in regression. Using matrix and optimization theory, we derive several theoretical results of K-optimal designs, including convexity of K-optimality criterion, lower bounds of the condition number, and symmetry properties of K-optimal designs. A general numerical method is developed to find K-optimal designs for any regression model on a discrete design space. In addition, specific results are obtained for polynomial, trigonometric and second-order response models.

Suggested Citation

  • Zongzhi Yue & Xiaoqing Zhang & P. van den Driessche & Julie Zhou, 2023. "Constructing K-optimal designs for regression models," Statistical Papers, Springer, vol. 64(1), pages 205-226, February.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:1:d:10.1007_s00362-022-01317-9
    DOI: 10.1007/s00362-022-01317-9
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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.
    2. A. Charnes & W. W. Cooper, 1962. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(3‐4), pages 181-186, September.
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