Statistical Inference for High-Dimensional Matrix-Variate Factor Models

• 成果类型: Article
• 署名作者: Chen, Elynn Y.; Fan, Jianqing
• 署名单位: University of California System; University of California Berkeley; Princeton University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.1970569
• 发表日期: 2023
• 页码: 1038-1055
• 关键词: Principal component analysis; Dynamic factor models; face representation; 2-dimensional pca; latent factors; number

摘要

This article considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates (p x q) is comparable to or greater than the number of observations (T). We propose an estimation method called alpha-PCA that preserves the matrix structure and aggregates mean and contemporary covariance through a hyper-parameter alpha. We develop an inferential theory, establishing consistency, the rate of convergence, and the limiting distributions, under general conditions that allow for correlations across time, rows, or columns of the noise. We show both theoretical and empirical methods of choosing the best alpha, depending on the use-case criteria. Simulation results demonstrate the adequacy of the asymptotic results in approximating the finite sample properties. The alpha-PCA compares favorably with the existing ones. Finally, we illustrate its applications with a real numeric dataset and two real image datasets. In all applications, the proposed estimation procedure outperforms previous methods in the power of variance explanation using out-of-sample 10-fold cross-validation. for this article are available online.