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Admissibility of linear estimators of the common mean parameter in general linear models under a balanced loss function

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  • Cao, Ming-Xiang
  • He, Dao-Jiang

Abstract

In order to investigate linearly admissible estimators of the common mean parameter in general linear models, we introduce and motivate the use of a balanced loss function obtained by combining Zellner’s idea of balanced loss (Zellner, 1994) with the unified theory of least squares (Rao, 1973). In classes of homogeneous and non-homogeneous linear estimators, sufficient and necessary conditions for linear estimators of the common mean parameter to be admissible are obtained, respectively. A comparison is then made between linearly admissible estimators and a “truly” unified least square estimator.

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  • Cao, Ming-Xiang & He, Dao-Jiang, 2017. "Admissibility of linear estimators of the common mean parameter in general linear models under a balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 246-254.
    • Handle: RePEc:eee:jmvana:v:153:y:2017:i:c:p:246-254
    DOI: 10.1016/j.jmva.2016.10.003
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    References listed on IDEAS

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    7. Cao, Mingxiang, 2014. "Admissibility of linear estimators for the stochastic regression coefficient in a general Gauss–Markoff model under a balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 25-30.
    8. Mohammad Jafari Jozani & Éric Marchand & Ahmad Parsian, 2012. "Bayesian and Robust Bayesian analysis under a general class of balanced loss functions," Statistical Papers, Springer, vol. 53(1), pages 51-60, February.
    9. He, Daojiang & Wu, Jie, 2014. "Admissible linear estimators of multivariate regression coefficient with respect to an inequality constraint under matrix balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 37-43.
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