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Equivariant Estimation

  • Robert W. Keener
Chapter
Part of the Springer Texts in Statistics book series (STS)

Abstract

In our study of UMVU estimation, we discovered that, for some models, if we restrict attention to the class of unbiased estimators there may be a best choice. Equivariant estimation is similar, but now we restrict attention to estimators that satisfy symmetry restrictions. At an abstract level, these restrictions are imposed using group theory. The basic ideas are developed here only for estimation of a location parameter, but we try to proceed in a fashion that illustrates the role of group theory.

Keywords

Loss Function Lebesgue Measure Location Parameter Risk Function Invariant Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer New York 2009

Authors and Affiliations

  • Robert W. Keener
    • 1
  1. 1.Department of StatisticsUniversity of MichiganAnn ArborUSA

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