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

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  • 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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