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On the equivalence of the BLUEs under a general linear model and its restricted and stochastically restricted models

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  • Ren, Xingwei

Abstract

Necessary and sufficient conditions are derived for the equalities of the best linear unbiased estimators (BLUEs) of parametric functions under a general linear model and its restricted and stochastically restricted models to hold.

Suggested Citation

  • Ren, Xingwei, 2014. "On the equivalence of the BLUEs under a general linear model and its restricted and stochastically restricted models," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 1-10.
    • Handle: RePEc:eee:stapro:v:90:y:2014:i:c:p:1-10
    DOI: 10.1016/j.spl.2014.03.006
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    References listed on IDEAS

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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. B. Ravikumar & Surajit Ray & N. Eugene Savin, 2000. "Robust Wald Tests in SUR Systems with Adding-up Restrictions," Econometrica, Econometric Society, vol. 68(3), pages 715-720, May.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Dent, Warren T., 1980. "On restricted estimation in linear models," Journal of Econometrics, Elsevier, vol. 12(1), pages 49-58, January.
    9. 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.
    10. Arashi, M. & Tabatabaey, S.M.M., 2008. "Stein-type improvement under stochastic constraints: Use of multivariate Student-t model in regression," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2142-2153, October.
    11. Harry Haupt & Walter Oberhofer, 2002. "Fully restricted linear regression: A pedagogical note," Economics Bulletin, AccessEcon, vol. 3(1), pages 1-7.
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    Cited by:

    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.

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