Factor Augmented Matrix Regression

• 成果类型: Article
• 署名作者: Chen, Elynn; Fan, Jianqing; Zhu, Xiaonan
• 署名单位: New York University; Princeton University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2025.2595734
• 发表日期: 2026-04-03
• 页码: 1192-1205
• 关键词: Diversified projections; FACTOR-AUGMENTED REGRESSION; High-dimensionality; Matrix factor models; Matrix regression; models; gdp

摘要

We introduce Factor-Augmented Matrix Regression (FAMAR) to address the growing applications of matrix-variate data and their associated challenges, particularly with high-dimensionality and covariate correlations. FAMAR encompasses two key algorithms. The first is a novel non-iterative approach that efficiently estimates the factors and loadings of the matrix factor model, using techniques of pre-training, diverse projection, and block-wise averaging. The second algorithm offers an accelerated solution for penalized matrix factor regression. Both algorithms are supported by established statistical and numerical convergence properties. Empirical evaluations conducted on synthetic and real economics datasets demonstrate FAMAR's superiority in terms of accuracy, interpretability, and computational speed. An application to economic data showcases how matrix factors can be incorporated to predict the GDPs of the countries of interest and the influence of these factors on the GDPs. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.