A Bayes Rule for Selecting the Largest Component.
CLEMSON UNIV SC DEPT OF MATHEMATICAL SCIENCES
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Let X subscript bar X subscript 1,...,X subscript k be a random vector whose distribution depends on an unknown vector parameter theta subscript bar theta subscript 1, theta subscript k. The marginal distribution of X subscript i depends on theta subscript i only, i 1,...,k. This paper deals with the problem of selecting the largest component of theta subscript bar and the analogous problem of selecting a subset of the components of theta subscript bar which includes the largest component. We consider the selection problem in a general decision theoretic framework and derive Bayes rules for selecting the largest component. The Bayes rules are shown to have certain optimal properties. The ordinary selection rules are shown to be Bayes rules, with respect to a special loss function. Author
- Statistics and Probability