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$$I_L$$ I L -optimal designs for regression models under the second-order least squares estimator

Author

Listed:
  • Lei He

    (Anhui Normal University)

  • Rong-Xian Yue

    (Shanghai Normal University)

Abstract

Compared with the ordinary least squares, the second-order least squares is a more efficient estimation method when the error distribution in a regression model is asymmetric. This paper is concerned with the problem of optimal regression designs based on the second-order least squares estimator under $$I_L$$ I L -optimality which emphasizes the designs to achieve reliable prediction from the fitted regression models. A general equivalence theorem for $$I_L$$ I L -optimality is established and used to check $$I_L$$ I L -optimality of designs. Invariant properties with respect to model reparameterization and linear transformation are also obtained. Several examples are given to illustrate the usefulness of these results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:1:d:10.1007_s00184-021-00819-0
    DOI: 10.1007/s00184-021-00819-0
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    References listed on IDEAS

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    1. S. Huda & Rahul Mukerjee, 2018. "Optimal designs with string property under asymmetric errors and SLS estimation," Statistical Papers, Springer, vol. 59(3), pages 1255-1268, September.
    2. Xin Chen & Min Tsao & Julie Zhou, 2012. "Robust second-order least-squares estimator for regression models," Statistical Papers, Springer, vol. 53(2), pages 371-386, May.
    3. 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.
    4. Masoudi, Ehsan & Holling, Heinz & Wong, Weng Kee, 2017. "Application of imperialist competitive algorithm to find minimax and standardized maximin optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 330-345.
    5. 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.
    6. 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.
    7. Dette, Holger & Biedermann, Stefanie, 2003. "Robust and Efficient Designs for the Michaelis-Menten Model," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 679-686, January.
    8. 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.
    9. D. Rosadi & P. Filzmoser, 2019. "Robust second-order least-squares estimation for regression models with autoregressive errors," Statistical Papers, Springer, vol. 60(1), pages 105-122, February.
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