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Linear Statistical Inference pp 150–161Cite as

Some Remarks on Improving Unbiased Estimators by Multiplication with a Constant

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Part of the book series: Lecture Notes in Statistics ((LNS,volume 35))

Summary

Using a general result due to Perlman (1972), we show that no invariant unbiased estimator for variance components (not necessarily being quadratic) qualifies to admissibility under the mean squared error risk function. Uniformly better estimates are easily given by multiplication of an unbiased estimator with some constant less than but close to one. The optimal choice of such a multiplier is investigated and more specific results are derived for quadratic estimation.

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References

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the GDR, Berlin, GDR

    J. Kleffe

Authors
  1. J. Kleffe
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Editor information

Editors and Affiliations

  1. Mathematical Institute, Polish Academy of Sciences, ul. Kopernika 18, 51-617, Wroclaw, Poland

    T. Caliński  & W. Klonecki  & 

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© 1985 Springer-Verlag Berlin Heidelberg

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Kleffe, J. (1985). Some Remarks on Improving Unbiased Estimators by Multiplication with a Constant. In: Caliński, T., Klonecki, W. (eds) Linear Statistical Inference. Lecture Notes in Statistics, vol 35. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-7353-1_12

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  • DOI: https://doi.org/10.1007/978-1-4615-7353-1_12

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96255-9

  • Online ISBN: 978-1-4615-7353-1

  • eBook Packages: Springer Book Archive

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