The Bayes rule of the parameter in (0,1) under Zhang’s loss function with an application to the beta-binomial model

Ying-Ying Zhang, Yu-Han Xie, Wen-He Song and Ming-Qin Zhou

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 8, 1904-1920

Abstract: 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).

Date: 2020
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DOI: 10.1080/03610926.2019.1565840

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