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Dispersion matrix comparisons among estimators under two competing restricted linear regression models

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  • Xingwei Ren

    (Anhui Science and Technology University)

  • Qian Zhou

    (Anhui Science and Technology University
    Wanjiang University of Technology)

Abstract

We consider two restricted linear regression models $${\mathscr {M}}_{1}$$ M 1 and $${\mathscr {M}}_{2}$$ M 2 , and obtain some conditons for the superiorities of the ordinary least squares estimators (OLSEs) and best linear unbiased estimators (BLUEs) under $${\mathscr {M}}_{1}$$ M 1 and $${\mathscr {M}}_{2}$$ M 2 with respect to the dispersion matrix criterion. Via these conditions, we provide an answer the question how to increase the estimation accuracy of related estimator by another one restriction.

Suggested Citation

  • Xingwei Ren & Qian Zhou, 2025. "Dispersion matrix comparisons among estimators under two competing restricted linear regression models," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(2), pages 601-614, June.
    • Handle: RePEc:spr:indpam:v:56:y:2025:i:2:d:10.1007_s13226-023-00505-z
    DOI: 10.1007/s13226-023-00505-z
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    References listed on IDEAS

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    1. Ren, Xingwei, 2016. "Estimation in singular linear models with stepwise inclusion of linear restrictions," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 60-72.
    2. Yongge Tian & Wenxing Guo, 2016. "On comparison of dispersion matrices of estimators under a constrained linear model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(4), pages 623-649, November.
    3. Guilkey, David K. & Price, J. Michael, 1981. "On comparing restricted least squares estimators," Journal of Econometrics, Elsevier, vol. 15(3), pages 397-404, April.
    4. 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.
    5. Y. Tian, 2017. "Some equalities and inequalities for covariance matrices of estimators under linear model," Statistical Papers, Springer, vol. 58(2), pages 467-484, June.
    6. 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.
    7. 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.
    8. Yongge Tian & Jie Wang, 2020. "Some remarks on fundamental formulas and facts in the statistical analysis of a constrained general linear model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(5), pages 1201-1216, March.
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