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

Lei He and Rong-Xian Yue ()
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Lei He: Anhui Normal University
Rong-Xian Yue: Shanghai Normal University

Metrika: International Journal for Theoretical and Applied Statistics, 2022, vol. 85, issue 1, No 3, 53-66

Abstract: 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.

Keywords: Optimal designs; Second-order least squares estimator; Predicted variance; General equivalence theorem; Invariance; 62K05 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00184-021-00819-0

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