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Equality of the BLUPs under the mixed linear model when random components and errors are correlated

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  • Liu, Xin
  • Wang, Qing-Wen

Abstract

We consider a general mixed linear model ℳ without any rank assumptions to the covariance matrix and without any restrictions on the correlation between the random effects vector and the random errors vector. We get the representations of best linear unbiased estimators (BLUEs)/ best linear unbiased predictors (BLUPs) of ℳ through a particular construction from the model ℳ which uses stochastic restriction. For the general mixed linear models ℳ1 and ℳ2, which have different covariance matrices, we derive the necessary and sufficient conditions for that the BLUEs and/or BLUPs under ℳ1 continue to be the BLUEs and/or BLUPs under the ℳ2. And we also give the necessary and sufficient conditions for the equivalence of BLUP under ℳ1 and ℳ2.

Suggested Citation

  • Liu, Xin & Wang, Qing-Wen, 2013. "Equality of the BLUPs under the mixed linear model when random components and errors are correlated," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 297-309.
    • Handle: RePEc:eee:jmvana:v:116:y:2013:i:c:p:297-309
    DOI: 10.1016/j.jmva.2012.12.006
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    References listed on IDEAS

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    1. Jian-Ying Rong & Xu-Qing Liu, 2010. "On misspecification of the dispersion matrix in mixed linear models," Statistical Papers, Springer, vol. 51(2), pages 445-453, June.
    2. Stephen Haslett & Simo Puntanen, 2011. "On the equality of the BLUPs under two linear mixed models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(3), pages 381-395, November.
    3. Liu, Xu-Qing & Rong, Jian-Ying & Liu, Xiu-Ying, 2008. "Best linear unbiased prediction for linear combinations in general mixed linear models," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1503-1517, September.
    4. 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.
    5. 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.
    6. 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.
    7. Stephen Haslett & Simo Puntanen, 2010. "Equality of BLUEs or BLUPs under two linear models using stochastic restrictions," Statistical Papers, Springer, vol. 51(2), pages 465-475, June.
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    Cited by:

    1. Samaradasa Weerahandi & Malwane Ananda, 2015. "Improving the EBLUPs of balanced mixed-effects models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(6), pages 647-662, August.
    2. S. J. Haslett & X. Q. Liu & A. Markiewicz & S. Puntanen, 2020. "Some properties of linear sufficiency and the BLUPs in the linear mixed model," Statistical Papers, Springer, vol. 61(1), pages 385-401, February.
    3. S. Haslett & S. Puntanen & B. Arendacká, 2015. "The link between the mixed and fixed linear models revisited," Statistical Papers, Springer, vol. 56(3), pages 849-861, August.

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