The Bayes rule of the parameter in \((0,1)\) under Zhang’s loss function with an application to the beta-binomial model. (English) Zbl 1511.62050
Summary: For the restricted parameter space \((0,1)\), we propose Zhang’s loss function which satisfies all the 7 properties for a good loss function on \((0,1)\). We then calculate the Bayes rule (estimator), the posterior expectation, the integrated risk, and the Bayes risk of the parameter in \((0,1)\) under Zhang’s loss function. We also calculate the usual Bayes estimator under the squared error loss function, and the Bayes estimator has been proved to underestimate the Bayes estimator under Zhang’s loss function. Finally, the numerical simulations and a real data example of some monthly magazine exposure data exemplify our theoretical studies of two size relationships about the Bayes estimators and the Posterior Expected Zhang’s Losses (PEZLs).
Keywords:
Bayes rule; restricted parameter space \((0,1)\); Zhang’s loss function; posterior expected loss; beta-binomial modelSoftware:
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