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D-optimal designs for a multidimensional second-degree polynomial model with no intercept

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  • Shpilev, P.V.

Abstract

The paper investigates the problem of constructing D-optimal designs for the multidimensional second-degree polynomial model without an intercept term. On a hyperparallelepiped of the given dimensionality and symmetric with respect to the origin, D-optimal designs are found in explicit analytical form.

Suggested Citation

  • Shpilev, P.V., 2024. "D-optimal designs for a multidimensional second-degree polynomial model with no intercept," Statistics & Probability Letters, Elsevier, vol. 215(C).
    • Handle: RePEc:eee:stapro:v:215:y:2024:i:c:s0167715224001974
    DOI: 10.1016/j.spl.2024.110228
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    References listed on IDEAS

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    1. Dette, Holger & Melas, Viatcheslav B. & Shpilev, Petr, 2021. "A note on optimal designs for estimating the slope of a polynomial regression," Statistics & Probability Letters, Elsevier, vol. 170(C).
    2. 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.
    3. Dette, Holger & Melas, Viatcheslav B. & Shpilev, Petr, 2020. "Optimal designs for estimating individual coefficients in polynomial regression with no intercept," Statistics & Probability Letters, Elsevier, vol. 158(C).
    4. Chang, Fu-Chuen, 1999. "Exact D-optimal designs for polynomial regression without intercept," Statistics & Probability Letters, Elsevier, vol. 44(2), pages 131-136, August.
    5. 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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