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The Bayes rule of the variance parameter of the hierarchical normal and inverse gamma model under Stein's loss

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  • Ying-Ying Zhang

Abstract

For the variance parameter of the hierarchical normal and inverse gamma model, we analytically calculate the Bayes rule (estimator) with respect to a prior distribution IG (alpha, beta) under Stein's loss function. This estimator minimizes the posterior expected Stein's loss (PESL). We also analytically calculate the Bayes rule and the PESL under the squared error loss. Finally, the numerical simulations exemplify that the PESLs depend only on alpha and the number of observations. The Bayes rules and PESLs under Stein's loss are unanimously smaller than those under the squared error loss.

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  • Ying-Ying Zhang, 2017. "The Bayes rule of the variance parameter of the hierarchical normal and inverse gamma model under Stein's loss," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(14), pages 7125-7133, July.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:14:p:7125-7133
    DOI: 10.1080/03610926.2016.1148733
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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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