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Some notes on linear sufficiency

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Abstract

In this paper we review some important aspects of the linear sufficiency of statistics \(\mathbf {F}\mathbf {y}\) and consider the relations of the best linear unbiased estimators of the estimable parametric functions under the linear model \(\fancyscript{A}\) and its counterpart \(\fancyscript{A}_{t}\) obtained by transforming \(\fancyscript{A}\) by the matrix \(\mathbf {F}\). 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.

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Acknowledgments

Sincere thanks go to Barbora Arendacká and Jarkko Isotalo for helpful discussions. The constructive comments of the referees are also gratefully acknowledged. Part of this research was done during the meeting of a Research Group on Mixed and Multivariate Models in the Mathematical Research and Conference Center, Bȩdlewo, Poland, October 2013, supported by the Stefan Banach International Mathematical Center.

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Authors and Affiliations

  1. Department of Mathematical and Statistical Methods, Poznań University of Life Sciences, Poznań, Poland

    Radosław Kala

  2. School of Information Sciences, University of Tampere, 33014, Tampere, Finland

    Simo Puntanen

  3. Central University of Finance and Economics, Beijing, 100081, China

    Yongge Tian

Authors
  1. Radosław Kala
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  2. Simo Puntanen
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  3. Yongge Tian
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Correspondence to Simo Puntanen.

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Kala, R., Puntanen, S. & Tian, Y. Some notes on linear sufficiency. Stat Papers 58, 1–17 (2017). https://doi.org/10.1007/s00362-015-0682-2

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  • DOI: https://doi.org/10.1007/s00362-015-0682-2

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