Unified improvements in estimation of a normal covariance matrix in high and low dimensions
Unified improvements in estimation of a normal covariance matrix in high and low dimensions
复制标题
高维和低维正态协方差矩阵估计的统一改进
DOI：
10.1016/j.jmva.2015.09.016
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发表时间：
2016
影响因子：
1.6
通讯作者：
T.
中科院分区：
文献类型：
--
作者：
Tsukuma;H. and Kubokawa;T.
在一个决策理论框架下讨论了多元线性回归模型中协方差矩阵的估计问题。本文在Stein-like损失下得到了与回归系数矩阵的维数、样本容量和秩无关的统一优势结果。特别地，利用Stein-Haff恒等式，我们得到了一个关键的不等式，它对于基于样本均值或回归系数的普通最小二乘估计中所包含的信息构造截断和改进的估计是有用的.此外，一个二次损失的功能是用来建议替代改进的估计相对于不变的二次损失。
The problem of estimating a covariance matrix in multivariate linear regression models is addressed in a decision-theoretic framework. This paper derives unified dominance results under a Stein-like loss, irrespective of order of the dimension, the sample size and the rank of the regression coefficients matrix. Especially, using the Stein–Haff identity, we develop a key inequality which is useful for constructing a truncated and improved estimator based on the information contained in the sample means or the ordinary least squares estimator of the regression coefficients. Also, a quadratic loss-like function is used to suggest alternative improved estimators with respect to an invariant quadratic loss.