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Singular value shrinkage priors for Bayesian prediction

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  • Takeru Matsuda
  • Fumiyasu Komaki

Abstract

We develop singular value shrinkage priors for the mean matrix parameters in the matrix-variate normal model with known covariance matrices. Our priors are superharmonic and put more weight on matrices with smaller singular values. They are a natural generalization of the Stein prior. Bayes estimators and Bayesian predictive densities based on our priors are minimax and dominate those based on the uniform prior in finite samples. In particular, our priors work well when the true value of the parameter has low rank.

Suggested Citation

  • Takeru Matsuda & Fumiyasu Komaki, 2015. "Singular value shrinkage priors for Bayesian prediction," Biometrika, Biometrika Trust, vol. 102(4), pages 843-854.
    • Handle: RePEc:oup:biomet:v:102:y:2015:i:4:p:843-854.
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    File URL: http://hdl.handle.net/10.1093/biomet/asv036
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    References listed on IDEAS

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    1. George, Edward I. & Xu, Xinyi, 2008. "Predictive Density Estimation For Multiple Regression," Econometric Theory, Cambridge University Press, vol. 24(2), pages 528-544, April.
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    Cited by:

    1. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2017. "Proper Bayes and minimax predictive densities related to estimation of a normal mean matrix," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 138-150.
    2. Matsuda, Takeru & Strawderman, William E., 2019. "Improved loss estimation for a normal mean matrix," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 300-311.
    3. Malay Ghosh & Tatsuya Kubokawa & Gauri Sankar Datta, 2020. "Density Prediction and the Stein Phenomenon," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 330-352, August.
    4. T Matsuda & W E Strawderman, 2022. "Estimation under matrix quadratic loss and matrix superharmonicity [Shrinkage estimation with a matrix loss function]," Biometrika, Biometrika Trust, vol. 109(2), pages 503-519.
    5. Matsuda, Takeru & Komaki, Fumiyasu, 2019. "Empirical Bayes matrix completion," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 195-210.
    6. Yuasa, Ryota & Kubokawa, Tatsuya, 2020. "Ridge-type linear shrinkage estimation of the mean matrix of a high-dimensional normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 178(C).

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