Core shrinkage covariance estimation for matrix-variate data
Core shrinkage covariance estimation for matrix-variate data
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DOI：
10.1093/jrsssb/qkad070
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发表时间：
2022-07
期刊：
影响因子：
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通讯作者：
P. Hoff;A. Mccormack;Anru R. Zhang
中科院分区：
文献类型：
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作者：
P. Hoff;A. Mccormack;Anru R. Zhang
可分离协方差模型可以描述随机矩阵的行间和列间相关性，并允许使用非常小的样本量进行基于似然的推断。但是，如果不满足可分离性假设，则使用可分离模型进行数据分析可能会歪曲数据中的重要依赖模式。作为可分离和非结构化协方差估计之间的折衷方案，我们将协方差矩阵分解为可分离分量和互补的“核心”协方差矩阵。该分解定义了一种新的协方差矩阵分解，它利用可分离协方差模型的简约性和可解释性，但完整地描述了不可分离的协方差矩阵。这种分解催生了一种新型的收缩估计器，它是通过适当收缩样本协方差矩阵的核心而获得的，它适应总体协方差矩阵的可分离程度。
A separable covariance model can describe the among-row and among-column correlations of a random matrix and permits likelihood-based inference with a very small sample size. However, if the assumption of separability is not met, data analysis with a separable model may misrepresent important dependence patterns in the data. As a compromise between separable and unstructured covariance estimation, we decompose a covariance matrix into a separable component and a complementary ‘core’ covariance matrix. This decomposition defines a new covariance matrix decomposition that makes use of the parsimony and interpretability of a separable covariance model, yet fully describes covariance matrices that are non-separable. This decomposition motivates a new type of shrinkage estimator, obtained by appropriately shrinking the core of the sample covariance matrix, that adapts to the degree of separability of the population covariance matrix.