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R-optimal designs for multi-factor models with heteroscedastic errors

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  • Lei He

    (Shanghai Normal University)

  • Rong-Xian Yue

    (Shanghai Normal University
    Scientific Computing Key Laboratory of Shanghai Universities)

Abstract

In this paper, we consider the R-optimal design problem for multi-factor regression models with heteroscedastic errors. It is shown that a R-optimal design for the heteroscedastic Kronecker product model is given by the product of the R-optimal designs for the marginal one-factor models. However, R-optimal designs for the additive models can be constructed from R-optimal designs for the one-factor models only if sufficient conditions are satisfied. Several examples are presented to illustrate and check optimal designs based on R-optimality criterion.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:80:y:2017:i:6:d:10.1007_s00184-017-0624-1
    DOI: 10.1007/s00184-017-0624-1
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    References listed on IDEAS

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    1. Xin Liu & Rong-Xian Yue, 2013. "A note on $$R$$ -optimal designs for multiresponse models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(4), pages 483-493, May.
    2. Carmelo Rodríguez & Isabel Ortiz & Ignacio Martínez, 2016. "A-optimal designs for heteroscedastic multifactor regression models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(3), pages 757-771, February.
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    4. Grace Montepiedra & Weng Wong, 2001. "A New Design Criterion When Heteroscedasticity is Ignored," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 418-426, June.
    5. S. Biedermann & H. Dette & D. C. Woods, 2011. "Optimal design for additive partially nonlinear models," Biometrika, Biometrika Trust, vol. 98(2), pages 449-458.
    6. Cun-Hui Zhang & Stephanie S. Zhang, 2014. "Confidence intervals for low dimensional parameters in high dimensional linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 217-242, January.
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    Cited by:

    1. 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.
    2. Min-Jue Zhang & Rong-Xian Yue, 2020. "Locally D-optimal designs for heteroscedastic polynomial measurement error models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 643-656, August.
    3. 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.
    4. Xin Liu & Rong-Xian Yue, 2020. "Elfving’s theorem for R-optimality of experimental designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(4), pages 485-498, May.
    5. Lei He & Rong-Xian Yue, 2020. "R-optimal designs for trigonometric regression models," Statistical Papers, Springer, vol. 61(5), pages 1997-2013, October.

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