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Bayesian predictive densities based on superharmonic priors for the 2-dimensional Wishart model

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  • Komaki, Fumiyasu

Abstract

Bayesian predictive densities for the 2-dimensional Wishart model are investigated. The performance of predictive densities is evaluated by using the Kullback-Leibler divergence. It is proved that a Bayesian predictive density based on a prior exactly dominates that based on the Jeffreys prior if the prior density satisfies some geometric conditions. An orthogonally invariant prior is introduced and it is shown that the Bayesian predictive density based on the prior is minimax and dominates that based on the right invariant prior with respect to the triangular group.

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  • Komaki, Fumiyasu, 2009. "Bayesian predictive densities based on superharmonic priors for the 2-dimensional Wishart model," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2137-2154, November.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:10:p:2137-2154
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    References listed on IDEAS

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    1. John C. Liechty, 2004. "Bayesian correlation estimation," Biometrika, Biometrika Trust, vol. 91(1), pages 1-14, March.
    2. James Zidek, 1969. "A representation of Bayes invariant procedures in terms of Haar measure," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 291-308, December.
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    1. Oda, Hidemasa & Komaki, Fumiyasu, 2023. "Enriched standard conjugate priors and the right invariant prior for Wishart distributions," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    2. T Sei & F Komaki, 2022. "A correlation-shrinkage prior for Bayesian prediction of the two-dimensional Wishart model [Modeling covariance matrices in terms of standard deviations and correlations, with application to shrink," Biometrika, Biometrika Trust, vol. 109(4), pages 1173-1180.

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