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Representations of best linear unbiased estimators in the Gauss-Markoff model with a singular dispersion matrix


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  • Rao, C. Radhakrishna
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    In the general Gauss-Markoff model (Y, X[beta], [sigma]2V), when V is singular, there exist linear functions of Y which vanish with probability 1 imposing some restrictions on Y as well as on the unknown [beta]. In all earlier work on linear estimation, representations of best-linear unbiased estimators (BLUE's) are obtained under the assumption: "L'Y is unbiased for X[beta] => L'X = X." Such a condition is not, however, necessary. The present paper provides all possible representations of the BLUE's some of which violate the condition L'X = X. Representations of X for given classes of BLUE's are also obtained.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 3 (1973)
    Issue (Month): 3 (September)
    Pages: 276-292

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    Handle: RePEc:eee:jmvana:v:3:y:1973:i:3:p:276-292

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    1. repec:ebl:ecbull:v:3:y:2002:i:1:p:1-7 is not listed on IDEAS
    2. Markiewicz, Augustyn, 1998. "Comparison of linear restricted models with respect to the validity of admissible and linearly sufficient estimators," Statistics & Probability Letters, Elsevier, vol. 38(4), pages 347-354, July.
    3. Changli Lu & Yuqin Sun & Yongge Tian, 2013. "On relations between weighted least-squares estimators of parametric functions under a general partitioned linear model and its small models," Metrika, Springer, vol. 76(5), pages 707-722, July.
    4. 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.
    5. 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.
    6. Gro[beta], J├╝rgen, 1998. "Statistical estimation by a linear combination of two given statistics," Statistics & Probability Letters, Elsevier, vol. 39(4), pages 379-384, August.


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