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Three strings of inequalities among six Bayes estimators

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

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.

Suggested Citation

  • Ying-Ying Zhang & Yu-Han Xie & Wen-He Song & Ming-Qin Zhou, 2018. "Three strings of inequalities among six Bayes estimators," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(8), pages 1953-1961, April.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:8:p:1953-1961
    DOI: 10.1080/03610926.2017.1335411
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    Cited by:

    1. Li Zhang & Ying-Ying Zhang, 2022. "The Bayesian Posterior and Marginal Densities of the Hierarchical Gamma–Gamma, Gamma–Inverse Gamma, Inverse Gamma–Gamma, and Inverse Gamma–Inverse Gamma Models with Conjugate Priors," Mathematics, MDPI, vol. 10(21), pages 1-27, October.

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