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Optimal and minimax prediction in multivariate normal populations under a balanced loss function

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  • Hu, Guikai
  • Li, Qingguo
  • Yu, Shenghua

Abstract

Under a balanced loss function, we investigate the optimal and minimax prediction of finite population regression coefficient in a general linear regression superpopulation model with normal errors. The best unbiased prediction (BUP) is obtained in the class of all unbiased predictors. The minimax predictor (MP) is also obtained in the class of all predictors. We prove that MP is unique in the class of all predictors and is better than BUP in a certain region of parameter space. Next, we give some conditions for optimality of the simple projection predictor (SPP) and prove that MP dominates SPP on certain occasions.

Suggested Citation

  • Hu, Guikai & Li, Qingguo & Yu, Shenghua, 2014. "Optimal and minimax prediction in multivariate normal populations under a balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 154-164.
    • Handle: RePEc:eee:jmvana:v:128:y:2014:i:c:p:154-164
    DOI: 10.1016/j.jmva.2014.03.014
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    References listed on IDEAS

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    1. Hu, Guikai & Peng, Ping, 2011. "All admissible linear estimators of a regression coefficient under a balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 102(8), pages 1217-1224, September.
    2. Ashok K. Bansal & Priyanka Aggarwal, 2009. "Bayes prediction of the regression coefficient in a finite population using balanced loss function," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 1-16.
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    Cited by:

    1. Peng, Ping & Hu, Guikai & Liang, Jian, 2015. "All admissible linear predictors in the finite populations with respect to inequality constraints under a balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 113-122.

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