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Optimal designs for minimax-criteria in random coefficient regression models

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  • Maryna Prus

    (Otto-von-Guericke University Magdeburg)

Abstract

We consider minimax-optimal designs for the prediction of individual parameters in random coefficient regression models. We focus on the minimax-criterion, which minimizes the “worst case” for the basic criterion with respect to the covariance matrix of random effects. We discuss particular models: linear and quadratic regression, in detail.

Suggested Citation

  • Maryna Prus, 2019. "Optimal designs for minimax-criteria in random coefficient regression models," Statistical Papers, Springer, vol. 60(2), pages 465-478, April.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:2:d:10.1007_s00362-018-01072-w
    DOI: 10.1007/s00362-018-01072-w
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    References listed on IDEAS

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    1. 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.
    2. Schwabe, Rainer, 1997. "Maximin efficient designs another view at D-optimality," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 109-114, September.
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    Cited by:

    1. Maryna Prus & Hans-Peter Piepho, 2021. "Optimizing the Allocation of Trials to Sub-regions in Multi-environment Crop Variety Testing," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(2), pages 267-288, June.
    2. 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.
    3. Lei He & Rong-Xian Yue, 2021. "D-optimal designs for hierarchical linear models with intraclass covariance structure," Statistical Papers, Springer, vol. 62(3), pages 1349-1361, June.
    4. Liu, Xin & Ye, Min & Yue, Rong-Xian, 2021. "Optimal designs for comparing population curves in hierarchical models," Statistics & Probability Letters, Elsevier, vol. 178(C).
    5. He, Lei & He, Daojiang, 2020. "R-optimal designs for individual prediction in random coefficient regression models," Statistics & Probability Letters, Elsevier, vol. 159(C).

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