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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 shrinkage]

Author

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  • T Sei
  • F Komaki

Abstract

SummaryA Bayesian prediction problem for the two-dimensional Wishart model is investigated within the framework of decision theory. The loss function is the Kullback–Leibler divergence. We construct a scale-invariant and permutation-invariant prior distribution that shrinks the correlation coefficient. The prior is the geometric mean of the right invariant prior with respect to permutation of the indices, and is characterized by a uniform distribution for Fisher’s -transformation of the correlation coefficient. The Bayesian predictive density based on the prior is shown to be minimax.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:109:y:2022:i:4:p:1173-1180.
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    References listed on IDEAS

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    1. 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.
    2. Michael J. Daniels & Robert E. Kass, 2001. "Shrinkage Estimators for Covariance Matrices," Biometrics, The International Biometric Society, vol. 57(4), pages 1173-1184, December.
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