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Some equalities for estimations of variance components in a general linear model and its restricted and transformed models


  • Tian, Yongge
  • Liu, Chunmei


For the unknown positive parameter [sigma]2 in a general linear model , the two commonly used estimations are the simple estimator (SE) and the minimum norm quadratic unbiased estimator (MINQUE). In this paper, we derive necessary and sufficient conditions for the equivalence of the SEs and MINQUEs of the variance component [sigma]2 in the original model [physics M-matrix (script capital m)], the restricted model , the transformed model , and the misspecified model .

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jmvana:v:101:y:2010:i:9:p:1959-1969

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    References listed on IDEAS

    1. Bassett, Gilbert W. & Koenker, Roger W., 1986. "Strong Consistency of Regression Quantiles and Related Empirical Processes," Econometric Theory, Cambridge University Press, vol. 2(02), pages 191-201, August.
    2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    3. C. M. Carvalho & J. G. Scott, 2009. "Objective Bayesian model selection in Gaussian graphical models," Biometrika, Biometrika Trust, vol. 96(3), pages 497-512.
    4. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
    5. Jianhua Hu & Valen E. Johnson, 2009. "Bayesian model selection using test statistics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 143-158.
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    Cited by:

    1. 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.


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