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D-optimal designs for polynomial regression models through origin

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  • Fang, Zhide

Abstract

In this article we consider D-optimal designs for polynomial regression models with low-degree terms being missed, by applying the theory of canonical moments. It turns out that the optimal design places equal weight on each of the zeros of some Jacobi polynomial when the number of unknown parameters in the model is even. The procedure and examples of finding the optimal supports and weights are given when the number of unknown parameters in the model is odd.

Suggested Citation

  • Fang, Zhide, 2002. "D-optimal designs for polynomial regression models through origin," Statistics & Probability Letters, Elsevier, vol. 57(4), pages 343-351, May.
    • Handle: RePEc:eee:stapro:v:57:y:2002:i:4:p:343-351
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    References listed on IDEAS

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    1. Chang, Fu-Chuen, 1999. "Exact D-optimal designs for polynomial regression without intercept," Statistics & Probability Letters, Elsevier, vol. 44(2), pages 131-136, August.
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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. Fang, Zhide, 2003. "D-optimal designs for weighted polynomial regression," Statistics & Probability Letters, Elsevier, vol. 63(2), pages 205-213, June.
    3. 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.
    4. Kim-Hung Li & Tai-Shing Lau & Chongqi Zhang, 2005. "A note on D-optimal designs for models with and without an intercept," Statistical Papers, Springer, vol. 46(3), pages 451-458, July.
    5. 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).

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    1. Kim-Hung Li & Tai-Shing Lau & Chongqi Zhang, 2005. "A note on D-optimal designs for models with and without an intercept," Statistical Papers, Springer, vol. 46(3), pages 451-458, July.
    2. 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).

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