Estimating a Covariance Matrix of a Normal Distribution with Unknown Mean
Estimating a Covariance Matrix of a Normal Distribution with Unknown Mean
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估计均值未知的正态分布的协方差矩阵
DOI：
10.11329/jjss1970.23.131
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
A. E. Saleh
中科院分区：
文献类型：
--
作者：
T. Kubokawa;Toshio Honda;K. Morita;A. E. Saleh
对于具有未知均值向量的多元正态分布的协方差阵，人们提出了间断或连续的Stein型截断估计。本文总结了最近的一系列结果，基于单变量情形下著名的Brown-Brewster-Zidek方法，得到了一个改进的广义Bayes估计，导出了估计的渐近风险展开式，并进行了数值研究，揭示了广义Bayes估计和经验Bayes估计在高维情形下的风险降低相当大.
For the covariance matrix of the multivariate normal distribution with an unknown mean vector, discontinuous or continuous Stein type truncated estimators have been proposed. This article summarizes a series of recent results and obtains an im proved and generalized Bayes estimator based on the Brown-Brewster-Zidek method, well known in the univariate case, The asymptotic risk expansions of the estimators are derived, numerically investigated, and it is revealed that the risk-reductions of the generalized Bayes estimator and an empirical Bayes estimator are considerably great in the large dimensional case.