Core shrinkage covariance estimation for matrix-variate data

• 成果类型: Article
• 署名作者: Hoff, Peter; McCormack, Andrew; Zhang, Anru R.
• 署名单位: Duke University; Duke University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkad070
• 发表日期: 2024
• 页码: 1659-1679
• 关键词: geodesic convexity; EXISTENCE; models; mle

摘要

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.