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Some explicit solutions of c-optimal design problems for polynomial regression with no intercept

Author

Listed:
  • Holger Dette

    (Ruhr-Universität Bochum)

  • Viatcheslav B. Melas

    (St. Petersburg State University)

  • Petr Shpilev

    (St. Petersburg State University)

Abstract

In this paper, we consider the optimal design problem for extrapolation and estimation of the slope at a given point, say z, in a polynomial regression with no intercept. We provide explicit solutions of these problems in many cases and characterize those values of z, where this is not possible.

Suggested Citation

  • Holger Dette & Viatcheslav B. Melas & Petr Shpilev, 2021. "Some explicit solutions of c-optimal design problems for polynomial regression with no intercept," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 61-82, February.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:1:d:10.1007_s10463-019-00736-0
    DOI: 10.1007/s10463-019-00736-0
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    References listed on IDEAS

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    1. Fang, Zhide, 2002. "D-optimal designs for polynomial regression models through origin," Statistics & Probability Letters, Elsevier, vol. 57(4), pages 343-351, May.
    2. Holger Dette & Mong-Na Lo Huang, 2000. "Convex Optimal Designs for Compound Polynomial Extrapolation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 557-573, September.
    3. Viatcheslav Melas & Andrey Pepelyshev & Russell Cheng, 2003. "Designs for estimating an extremal point of quadratic regression models in a hyperball," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(2), pages 193-208, September.
    Full references (including those not matched with items on IDEAS)

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