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Some notes on linear sufficiency

Author

Listed:
  • Radosław Kala

    (Poznań University of Life Sciences)

  • Simo Puntanen

    (University of Tampere)

  • Yongge Tian

    (Central University of Finance and Economics)

Abstract

In this paper we review some important aspects of the linear sufficiency of statistics $$\mathbf {F}\mathbf {y}$$ F y and consider the relations of the best linear unbiased estimators of the estimable parametric functions under the linear model $$\fancyscript{A}$$ A and its counterpart $$\fancyscript{A}_{t}$$ A t obtained by transforming $$\fancyscript{A}$$ A by the matrix $$\mathbf {F}$$ F . Most results obtained appear in literature but often in scattered form. Our aim is provide a concise view of this problem area and discuss some possible misunderstandings.

Suggested Citation

  • Radosław Kala & Simo Puntanen & Yongge Tian, 2017. "Some notes on linear sufficiency," Statistical Papers, Springer, vol. 58(1), pages 1-17, March.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:1:d:10.1007_s00362-015-0682-2
    DOI: 10.1007/s00362-015-0682-2
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    References listed on IDEAS

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    1. Gourieroux, Christian & Monfort, Alain, 1980. "Sufficient Linear Structures: Econometric Applications," Econometrica, Econometric Society, vol. 48(5), pages 1083-1097, July.
    2. Radosław Kala & Paweł Pordzik, 2009. "Estimation in singular partitioned, reduced or transformed linear models," Statistical Papers, Springer, vol. 50(3), pages 633-638, June.
    3. Michael C. Lovell, 1963. "Seasonal Adjustment of Economic Time Series and Multiple Regression," Cowles Foundation Discussion Papers 151, Cowles Foundation for Research in Economics, Yale University.
    4. Jürgen Groß, 2004. "The general Gauss-Markov model with possibly singular dispersion matrix," Statistical Papers, Springer, vol. 45(3), pages 311-336, July.
    5. Oskar Baksalary & Götz Trenkler, 2009. "A projector oriented approach to the best linear unbiased estimator," Statistical Papers, Springer, vol. 50(4), pages 721-733, August.
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    Cited by:

    1. Yongge Tian, 2017. "Transformation approaches of linear random-effects models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 583-608, November.
    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.

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