A unified approach to estimating a normal mean matrix in high and low dimensions
A unified approach to estimating a normal mean matrix in high and low dimensions
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DOI：
10.1016/j.jmva.2015.04.003
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发表时间：
2015-07
期刊：
影响因子：
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通讯作者：
Hisayuki Tsukuma;T. Kubokawa
中科院分区：
文献类型：
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作者：
Hisayuki Tsukuma;T. Kubokawa
本文研究了用未知协方差矩阵估计正态均值矩阵的问题。在经验贝叶斯方法的激励下，我们提出了一种基于Moore-Penrose逆的Efron-Morris型估计的统一形式。这种形式不仅可以定义为任何维度和任何样本量，而且可以包含迄今为止文献中建议的Efron-Morris型或Baranchik型估计量。此外，统一的形式提出了一般类别的收缩估计。对于一般类内的收缩估计量，导出了与协方差矩阵维数和平均矩阵大小无关的风险函数无偏估计量的统一表达式。给出了收缩估计器的正部分规则的解析优势性结果。
This paper addresses the problem of estimating the normal mean matrix with an unknown covariance matrix. Motivated by an empirical Bayes method, we suggest a unified form of the Efron–Morris type estimators based on the Moore–Penrose inverse. This form not only can be defined for any dimension and any sample size, but also can contain the Efron–Morris type or Baranchik type estimators suggested so far in the literature. Also, the unified form suggests a general class of shrinkage estimators. For shrinkage estimators within the general class, a unified expression of unbiased estimators of the risk functions is derived regardless of the dimension of covariance matrix and the size of the mean matrix. An analytical dominance result is provided for a positive-part rule of the shrinkage estimators.