Three strings of inequalities among six Bayes estimators

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

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 8, 1953-1961

Abstract: We discover three interesting strings of inequalities among six Bayes estimators, where for the parameter space (0, 1), (0, ∞), and ( − ∞, ∞), each case has a string of inequalities. The three strings of inequalities only depend on the loss functions, and the inequalities are independent of the chosen models and the used priors provided the Bayes estimators exist. Therefore, they exist in a general setting which makes them quite interesting. Finally, the numerical simulations exemplify the two strings of inequalities defined on (0, 1) and (0, ∞), and that there does not exist a string of inequalities among the six smallest posterior expected losses.

Date: 2018
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DOI: 10.1080/03610926.2017.1335411

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