Proper Bayes and minimax predictive densities related to estimation of a normal mean matrix
Proper Bayes and minimax predictive densities related to estimation of a normal mean matrix
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与正态平均矩阵估计相关的适当贝叶斯和极小极大预测密度
DOI：
10.1016/j.jmva.2017.05.004
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发表时间：
2017
影响因子：
1.6
通讯作者：
Tatsuya Kubokawa
中科院分区：
文献类型：
--
作者：
Hisayuki Tsukuma;Tatsuya Kubokawa
本文讨论了已知协方差阵的矩阵变量正态分布的预测密度估计问题。我们的主要目的是建立一些贝叶斯预测密度相关的矩阵收缩估计的正态均值矩阵。Kullback-Leibler损失用于评估预测密度的决策理论最优性。它表明，一个适当的分层先验产生一个容许的和极大极小的预测密度。此外，一些极大极小预测密度是从先验密度的超调和性推导出来的。
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-theoretic optimality of predictive densities. It is shown that a proper hierarchical prior yields an admissible and minimax predictive density. Also, some minimax predictive densities are derived from superharmonicity of prior densities.