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Some remarks on general linear model with new regressors

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  • Lu, Changli
  • Gan, Shengjun
  • Tian, Yongge

Abstract

Assume that an original general linear model is misspecified by adding some new regressors. We investigate in such a case relationships between the best linear unbiased estimators under the two models. In particular, we give necessary and sufficient conditions for the best linear unbiased estimators to be equal under the two models.

Suggested Citation

  • Lu, Changli & Gan, Shengjun & Tian, Yongge, 2015. "Some remarks on general linear model with new regressors," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 16-24.
    • Handle: RePEc:eee:stapro:v:97:y:2015:i:c:p:16-24
    DOI: 10.1016/j.spl.2014.10.015
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Tian, Yongge & Takane, Yoshio, 2008. "Some properties of projectors associated with the WLSE under a general linear model," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1070-1082, July.
    5. 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.
    6. 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.
    7. Jammalamadaka, S. Rao & Sengupta, D., 2007. "Inclusion and exclusion of data or parameters in the general linear model," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1235-1247, July.
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    Cited by:

    1. Bo Jiang & Yongge Tian, 2022. "Equivalence Analysis of Statistical Inference Results under True and Misspecified Multivariate Linear Models," Mathematics, MDPI, vol. 11(1), pages 1-16, December.
    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. 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.

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