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R-optimal designs for individual prediction in random coefficient regression models

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  • He, Lei
  • He, Daojiang

Abstract

In this paper we consider optimal designs for the R-criterion in random coefficient regression models. We derive two equivalence theorems to characterize the optimal designs for the prediction of the individual parameters and for the individual deviations from the unknown population mean parameters in random coefficient models. Some examples of the R-optimal designs for the straight line regression with random coefficients are presented for illustration.

Suggested Citation

  • He, Lei & He, Daojiang, 2020. "R-optimal designs for individual prediction in random coefficient regression models," Statistics & Probability Letters, Elsevier, vol. 159(C).
    • Handle: RePEc:eee:stapro:v:159:y:2020:i:c:s016771521930330x
    DOI: 10.1016/j.spl.2019.108684
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    References listed on IDEAS

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    1. Maryna Prus, 2019. "Optimal designs for minimax-criteria in random coefficient regression models," Statistical Papers, Springer, vol. 60(2), pages 465-478, April.
    2. Thomas Schmelter, 2007. "The Optimality of Single-group Designs for Certain Mixed Models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(2), pages 183-193, February.
    3. Xin Liu & Rong-Xian Yue & Weng Kee Wong, 2019. "D-optimal designs for multi-response linear mixed models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 87-98, January.
    4. Maryna Prus & Rainer Schwabe, 2016. "Optimal designs for the prediction of individual parameters in hierarchical models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 175-191, January.
    5. 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.
    6. Liu, Xin & Yue, Rong-Xian & Chatterjee, Kashinath, 2014. "R-optimal designs in random coefficient regression models," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 127-132.
    7. Prus, Maryna, 2019. "Various optimality criteria for the prediction of individual response curves," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 36-41.
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    Cited by:

    1. Xin Liu & Rong‐Xian Yue & Weng Kee Wong, 2022. "Equivalence theorems for c and DA‐optimality for linear mixed effects models with applications to multitreatment group assignments in health care," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1842-1859, December.

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