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Properties of optimal regression designs under the second-order least squares estimator

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  • Chi-Kuang Yeh

    (University of Victoria)

  • Julie Zhou

    (University of Victoria)

Abstract

We investigate properties of optimal designs under the second-order least squares estimator (SLSE) for linear and nonlinear regression models. First we derive equivalence theorems for optimal designs under the SLSE. We then obtain the number of support points in A-, c- and D-optimal designs analytically for several models. Using a generalized scale invariance concept we also study the scale invariance property of D-optimal designs. In addition, numerical algorithms are discussed for finding optimal designs. The results are quite general and can be applied for various linear and nonlinear models. Several applications are presented, including results for fractional polynomial, spline regression and trigonometric regression models.

Suggested Citation

  • Chi-Kuang Yeh & Julie Zhou, 2021. "Properties of optimal regression designs under the second-order least squares estimator," Statistical Papers, Springer, vol. 62(1), pages 75-92, February.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:1:d:10.1007_s00362-018-01076-6
    DOI: 10.1007/s00362-018-01076-6
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    References listed on IDEAS

    as
    1. Liqun Wang & Alexandre Leblanc, 2008. "Second-order nonlinear least squares estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(4), pages 883-900, December.
    2. Dette, Holger & Melas, Viatcheslav B. & Wong, Weng Kee, 2005. "Optimal Design for Goodness-of-Fit of the MichaelisMenten Enzyme Kinetic Function," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1370-1381, December.
    3. Lucy L. Gao & Julie Zhou, 2017. "D-optimal designs based on the second-order least squares estimator," Statistical Papers, Springer, vol. 58(1), pages 77-94, March.
    Full references (including those not matched with items on IDEAS)

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