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arXiv · 1703.10393

Proper Bayes and Minimax Predictive Densities for a Matrix-variate Normal Distribution

Hisayuki Tsukuma·Tatsuya Kubokawa
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Abstract

This paper deals with the problem of estimating predictive densities of a matrix-variate normal distribution with known covariance matrix. Our main aim is to establish some Bayesian predictive densities related to matricial shrinkage estimators of the normal mean matrix. The Kullback-Leibler loss is used for evaluating decision-theoretical optimality of predictive densities. It is shown that a proper hierarchical prior yields an admissible and minimax predictive density. Also, superharmonicity of prior densities is paid attention to for finding out a minimax predictive density with good numerical performance.

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Hisayuki Tsukuma, Tatsuya Kubokawa. 2017-03-30. Proper Bayes and Minimax Predictive Densities for a Matrix-variate Normal Distribution. https://arxiv.org/abs/1703.10393

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