论文标题
核心收缩协方差估计矩阵变化数据
Core Shrinkage Covariance Estimation for Matrix-variate Data
论文作者
论文摘要
一个随机矩阵的可分离协方差模型提供了对行之间的协方差和矩阵列之间的简约描述，并允许基于可能的可能的推理具有很小的样本尺寸。但是，在许多应用中，不太可能实现确切可分离性的假设，并且具有可分离模型的数据分析可能会忽略数据中的重要依赖模式。在本文中，我们提出了可分离和非结构化协方差估计之间的妥协。我们展示了如何根据可分离的协方差矩阵和互补的“核心”协方差矩阵来唯一地参数的协方差矩阵，其中可分离协方差矩阵的核心是身份矩阵。该参数化定义了协方差矩阵的kronecker核核分解。通过使用经验贝叶斯程序缩小样品协方差矩阵的核心，我们获得了一个可以适应种群协方差矩阵的可分离性程度的估计器。
A separable covariance model for a random matrix provides a parsimonious description of the covariances among the rows and among the columns of the matrix, and permits likelihood-based inference with a very small sample size. However, in many applications the assumption of exact separability is unlikely to be met, and data analysis with a separable model may overlook or misrepresent important dependence patterns in the data. In this article, we propose a compromise between separable and unstructured covariance estimation. We show how the set of covariance matrices may be uniquely parametrized in terms of the set of separable covariance matrices and a complementary set of "core" covariance matrices, where the core of a separable covariance matrix is the identity matrix. This parametrization defines a Kronecker-core decomposition of a covariance matrix. By shrinking the core of the sample covariance matrix with an empirical Bayes procedure, we obtain an estimator that can adapt to the degree of separability of the population covariance matrix.
