Annals of the Institute of Statistical Mathematics

, Volume 21, Issue 1, pp 457–469

# Locally averaged risk

• Khursheed Alam
• James R. Thompson
Article

## 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.

## Keywords

Decision Rule Loss Function Prior Distribution Risk Function Usual Estimate
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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