Locally averaged risk
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.
KeywordsDecision Rule Loss Function Prior Distribution Risk Function Usual Estimate
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