Statistical Inference for High-Dimensional Matrix-Variate Factor Models

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 × q) is comparable to or greater than the number of observations (T). We propose an estimation method called α-PCA that pres...

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Bibliographic Details
Published in:Journal of the American Statistical Association Vol. 118; no. 542; pp. 1038 - 1055
Main Authors: Chen, Elynn Y., Fan, Jianqing
Format: Journal Article
Language:English
Published: Alexandria Taylor & Francis 03.04.2023
Taylor & Francis Ltd
Subjects:
Adequacy
Analysis of covariance
Asymptotic normality
Convergence
covariance
data collection
Datasets
Estimation
Factor models
High-dimension
Inference
Latent low rank
Matrix-variate
Property
Regression analysis
Research methodology
Simulation
Statistical inference
Statistical methods
Statistics
variance
ISSN:0162-1459, 1537-274X, 1537-274X
Online Access:Get full text
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Summary: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 × q) is comparable to or greater than the number of observations (T). We propose an estimation method called α-PCA that preserves the matrix structure and aggregates mean and contemporary covariance through a hyper-parameter α. 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 α, depending on the use-case criteria. Simulation results demonstrate the adequacy of the asymptotic results in approximating the finite sample properties. The α-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. Supplementary materials for this article are available online.
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ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2021.1970569