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Locally averaged risk

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Summary

A heuristic method of reducing a class of admissible or Bayes decision rules is given. A new risk function is defined which is called the locally averaged risk. Bayes and admissible rules with respect to the new risk function are calledG-Bayes andG-admissible, respectively. It is shown under general assumptions that the class ofG-Bayes decision rules is a subset of the class of Bayes decision rules and the class ofG-admissible decision rules is a subset of the class of admissible decision rules.

Some examples are considered, showing that the usual estimates of the parameter of a distribution with squared error as loss function, which are known to be admissible, are alsoG-admissible.

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Author information

Authors and Affiliations

  1. Indiana University, Indiana, USA

    Khursheed Alam & James R. Thompson

Authors
  1. Khursheed Alam
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  2. James R. Thompson
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Additional information

This work was supported in part by NASA Grant-NGR 15-003-064 and NSF Grant-GP 7496 at Indiana University.

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Alam, K., Thompson, J.R. Locally averaged risk. Ann Inst Stat Math 21, 457–469 (1969). https://doi.org/10.1007/BF02532271

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  • DOI: https://doi.org/10.1007/BF02532271

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