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Optimal designs for multi-factor nonlinear models based on the second-order least squares estimator

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  • He, Lei

Abstract

In this paper, we investigate the locally and maximin optimal design problems for multi-factor nonlinear models based on the second-order least squares estimator (SLSE), it is shown that the product-type designs are optimal based on the SLSE for the multi-factor nonlinear models without constant term when the sufficient conditions are satisfied. Some examples are presented to illustrate the theoretical results. Several by-products on locally and maximin optimal designs for uni-factor exponential decay models are also obtained.

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  • He, Lei, 2018. "Optimal designs for multi-factor nonlinear models based on the second-order least squares estimator," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 201-208.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:201-208
    DOI: 10.1016/j.spl.2018.01.005
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    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. Holger Dette, 1997. "Designing Experiments with Respect to ‘Standardized’ Optimality Criteria," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 97-110.
    3. Lei He & Rong-Xian Yue, 2017. "R-optimal designs for multi-factor models with heteroscedastic errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 717-732, November.
    4. S. Biedermann & H. Dette & D. C. Woods, 2011. "Optimal design for additive partially nonlinear models," Biometrika, Biometrika Trust, vol. 98(2), pages 449-458.
    5. 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.
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    1. Lei He, 2021. "Bayesian optimal designs for multi-factor nonlinear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 223-233, March.
    2. Lei He & Rong-Xian Yue, 2022. "$$I_L$$ I L -optimal designs for regression models under the second-order least squares estimator," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(1), pages 53-66, January.

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