Nonparametric Bayes Estimation with Incomplete Dirichlet Prior Information.
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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Typically, to use estimators which are Bayes with respect to Fergusons Dirichlet process prior, the statistician must provide a complete specification of the process parameter alpha, a non-negative non-null finite measure on a measureable space X, A. Here we take X R, the real line, and A B the Borel sigma-field. Mixed rules rules which minimize the average maximum risk are derived for estimating PrX or Y and for estimating rank order. These estimators are incomplete information analogues of Fergusons Bayes estimator of PrX or Y and the Campbell-Hollander Bayes estimator of rank order.
- Statistics and Probability