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Some overall properties of seemingly unrelated regression models

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  • Yuqin Sun
  • Rong Ke
  • Yongge Tian

Abstract

Seemingly unrelated regression models are extensions of linear regression models which allow correlated errors between equations. Estimations and inferences of singular seemingly unrelated regression models involve some complicated operations of the given matrices in the models and their generalized inverses. In this study, we characterize the consistency, natural restrictions, estimability of parametric functions under a singular seemingly unrelated regression model using the matrix rank method. We also derive necessary and sufficient conditions for the ordinary least squares estimators and the best linear unbiased estimators of parametric functions to be equal under seemingly unrelated regression models. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Yuqin Sun & Rong Ke & Yongge Tian, 2014. "Some overall properties of seemingly unrelated regression models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 103-120, April.
    • Handle: RePEc:spr:alstar:v:98:y:2014:i:2:p:103-120
    DOI: 10.1007/s10182-013-0212-2
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    1. repec:ebl:ecbull:v:3:y:2002:i:1:p:1-7 is not listed on IDEAS
    2. Yongge Tian & M. Beisiegel & E. Dagenais & C. Haines, 2008. "On the natural restrictions in the singular Gauss–Markov model," Statistical Papers, Springer, vol. 49(3), pages 553-564, July.
    3. Puntanen, Simo & Styan, George P.H. & Tian, Yongge, 2005. "Three Rank Formulas Associated With The Covariance Matrices Of The Blue And The Olse In The General Linear Model," Econometric Theory, Cambridge University Press, vol. 21(3), pages 659-663, June.
    4. Jürgen Groß, 2004. "The general Gauss-Markov model with possibly singular dispersion matrix," Statistical Papers, Springer, vol. 45(3), pages 311-336, July.
    5. Phillips, Peter C. B., 1977. "An approximation to the finite sample distribution of Zellner's seemingly unrelated regression estimator," Journal of Econometrics, Elsevier, vol. 6(2), pages 147-164, September.
    6. Baksalary, Jerzy K. & Trenkler, Götz, 1989. "The Efficiency of OLS in a Seemingly Unrelated Regressions Model," Econometric Theory, Cambridge University Press, vol. 5(03), pages 463-465, December.
    7. 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.
    8. Qian, Hailong & Schmidt, Peter, 2003. "Partial GLS regression," Economics Letters, Elsevier, vol. 79(3), pages 385-392, June.
    9. Qian, Hailong & Tian, Yongge, 2006. "Partially Superfluous Observations," Econometric Theory, Cambridge University Press, vol. 22(3), pages 529-536, June.
    10. Tian, Yongge & Liu, Chunmei, 2010. "Some equalities for estimations of variance components in a general linear model and its restricted and transformed models," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1959-1969, October.
    11. Yongge Tian, 2010. "Weighted least-squares estimators of parametric functions of the regression coefficients under a general linear model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(5), pages 929-941, October.
    12. Harry Haupt & Walter Oberhofer, 2002. "Fully restricted linear regression: A pedagogical note," Economics Bulletin, AccessEcon, vol. 3(1), pages 1-7.
    13. Tian, Yongge, 2009. "On an additive decomposition of the BLUE in a multiple-partitioned linear model," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 767-776, April.
    14. 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.
    15. Tian, Yongge & Wiens, Douglas P., 2006. "On equality and proportionality of ordinary least squares, weighted least squares and best linear unbiased estimators in the general linear model," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1265-1272, July.
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    Cited by:

    1. Jiang, Hong & Qian, Jianwei & Sun, Yuqin, 2020. "Best linear unbiased predictors and estimators under a pair of constrained seemingly unrelated regression models," Statistics & Probability Letters, Elsevier, vol. 158(C).
    2. Nesrin Güler & Melek Eriş Büyükkaya & Melike Yiğit, 2022. "Comparison of Covariance Matrices of Predictors in Seemingly Unrelated Regression Models," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(3), pages 801-809, September.
    3. Shun Matsuura & Hiroshi Kurata, 2022. "Optimal estimator under risk matrix in a seemingly unrelated regression model and its generalized least squares expression," Statistical Papers, Springer, vol. 63(1), pages 123-141, February.
    4. Haithem Awijen & Younes Ben Zaied & Ahmed Imran Hunjra, 2023. "Systematic and Unsystematic Determinants of Sectoral Risk Default Interconnectedness," Computational Economics, Springer;Society for Computational Economics, vol. 62(2), pages 561-587, August.

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