Estimation of a high-dimensional covariance matrix with the Stein loss
Estimation of a high-dimensional covariance matrix with the Stein loss
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DOI：
10.1016/j.jmva.2016.02.012
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发表时间：
2016-06-01
影响因子：
1.6
通讯作者：
Tsukuma, Hisayuki
中科院分区：
文献类型：
--
作者：
Tsukuma, Hisayuki
从决策论的角度考虑了正态协方差矩阵的估计问题，其中协方差矩阵的维数大于样本容量。本文不仅讨论了非奇异的情况下，但也奇异的情况下的协方差矩阵。基于James和Stein的极大极小估计和正交不变估计，对协方差矩阵的维数、样本容量和秩的任何可能的排序，统一定义了几类估计.统一的优势，这样的类的结果下提供斯坦型熵损失。统一优势的结果被应用到改进的经验贝叶斯估计的高维协方差矩阵。(c)2016 Elsevier Inc. All rights reserved.
The problem of estimating a normal covariance matrix is considered from a decision theoretic point of view, where the dimension of the covariance matrix is larger than the sample size. This paper addresses not only the nonsingular case but also the singular case in terms of the covariance matrix. Based on James and Stein's minimax estimator and on an orthogonally invariant estimator, some classes of estimators are unifiedly defined for any possible ordering on the dimension, the sample size and the rank of the covariance matrix. Unified dominance results on such classes are provided under a Stein-type entropy loss. The unified dominance results are applied to improving on an empirical Bayes estimator of a high-dimensional covariance matrix. (c) 2016 Elsevier Inc. All rights reserved.