Minimax estimation of a normal covariance matrix with the partial Iwasawa decomposition
Minimax estimation of a normal covariance matrix with the partial Iwasawa decomposition
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DOI：
10.1016/j.jmva.2015.12.013
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发表时间：
2016-03
期刊：
影响因子：
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通讯作者：
Hisayuki Tsukuma
中科院分区：
文献类型：
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作者：
Hisayuki Tsukuma
本文讨论的问题，估计正常的协方差矩阵相对于斯坦损失。部分岩泽分解用于减少原来的估计问题，同时估计一些正态分布的方差和均值。方差和平均值分别与协方差矩阵的Cholesky分解得到的下三角矩阵的对角元素和下对角元素密切相关。收缩型程序提出的改进不仅对对角元素，而且对对角元素对应的James和Stein极大极小估计的协方差矩阵。
This paper addresses the problem of estimating the normal covariance matrix relative to the Stein loss. The partial Iwasawa decomposition is used to reduce the original estimation problem to simultaneous estimation for variances and means of some normal distributions. The variances and the means are closely related to, respectively, the diagonal and the below-diagonal elements of a lower triangular matrix which is made from the Cholesky decomposition of the covariance matrix. Shrinkage type procedures are proposed for improvements not only on the diagonal elements but also on the below-diagonal elements corresponding to the James and Stein minimax estimator of the covariance matrix.