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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. 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.
    2. Gourieroux, Christian & Monfort, Alain, 1980. "Sufficient Linear Structures: Econometric Applications," Econometrica, Econometric Society, vol. 48(5), pages 1083-1097, July.
    3. Radosław Kala & Paweł Pordzik, 2009. "Estimation in singular partitioned, reduced or transformed linear models," Statistical Papers, Springer, vol. 50(3), pages 633-638, June.
    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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