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On the equality of estimators under a general partitioned linear model with parameter restrictions

Author

Listed:
  • Bo Jiang

    (Shandong Institute of Business and Technology)

  • Yuqin Sun

    (Shanghai Maritime University)

Abstract

Assume that a linear regression model is written as a partitioned form. In such a case, it is quite convenient to determine the role of each subset of regressors, and to derive estimators of unknown partial parameters in the partitioned model. In this paper, we consider the relationships between the well-known ordinary least-squares estimators (OLSEs) and the best linear unbiased estimators (BLUEs) of the whole and partial mean parameter vectors in a general partitioned linear model with parameter restrictions. We first review some known results on the OLSEs and the BLUEs and their properties under general linear models. We then present a variety of necessary and sufficient conditions for OLSEs to be BLUEs under a general partitioned linear model with parameter restrictions.

Suggested Citation

  • Bo Jiang & Yuqin Sun, 2019. "On the equality of estimators under a general partitioned linear model with parameter restrictions," Statistical Papers, Springer, vol. 60(1), pages 273-292, February.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:1:d:10.1007_s00362-016-0837-9
    DOI: 10.1007/s00362-016-0837-9
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    References listed on IDEAS

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    1. Jarkko Isotalo & Simo Puntanen, 2009. "A note on the equality of the OLSE and the BLUE of the parametric function in the general Gauss–Markov model," Statistical Papers, Springer, vol. 50(1), pages 185-193, January.
    2. Tian, Yongge & Jiang, Bo, 2016. "Equalities for estimators of partial parameters under linear model with restrictions," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 299-313.
    3. Yongge Tian, 2007. "Some Decompositions of OLSEs and BLUEs Under a Partitioned Linear Model," International Statistical Review, International Statistical Institute, vol. 75(2), pages 224-248, August.
    4. Stephen Haslett & Jarkko Isotalo & Yonghui Liu & Simo Puntanen, 2014. "Equalities between OLSE, BLUE and BLUP in the linear model," Statistical Papers, Springer, vol. 55(2), pages 543-561, May.
    5. Tian, Yongge & Zhang, Xuan, 2016. "On connections among OLSEs and BLUEs of whole and partial parameters under a general linear model," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 105-112.
    6. Yongge Tian & Jieping Zhang, 2011. "Some equalities for estimations of partial coefficients under a general linear regression model," Statistical Papers, Springer, vol. 52(4), pages 911-920, November.
    7. Yongge Tian, 2010. "On equalities of estimations of parametric functions under a general linear model and its restricted models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(3), pages 313-330, November.
    8. Rao, C. Radhakrishna, 1973. "Representations of best linear unbiased estimators in the Gauss-Markoff model with a singular dispersion matrix," Journal of Multivariate Analysis, Elsevier, vol. 3(3), pages 276-292, September.
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