Improved prediction for a multivariate normal distribution with unknown mean and variance
Improved prediction for a multivariate normal distribution with unknown mean and variance
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改进了均值和方差未知的多元正态分布的预测
DOI：
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发表时间：
2009
期刊：
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通讯作者：
Kengo Kato
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文献类型：
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作者：
Kengo Kato
考虑均值和方差均未知的多元正态分布的预测问题。当使用 Kullback-Leibler 损失时，基于右不变先验的贝叶斯预测密度（结果是多元 t 分布的密度）是最佳不变性和极小极大预测密度。在本文中，我们引入了不适当的收缩先验，并表明当维度大于或等于三时，针对收缩先验的贝叶斯预测密度优于最佳不变预测密度。
The prediction problem for a multivariate normal distribution is considered where both mean and variance are unknown. When the Kullback–Leibler loss is used, the Bayesian predictive density based on the right invariant prior, which turns out to be a density of a multivariate t-distribution, is the best invariant and minimax predictive density. In this paper, we introduce an improper shrinkage prior and show that the Bayesian predictive density against the shrinkage prior improves upon the best invariant predictive density when the dimension is greater than or equal to three.