Statistical Inference for High-Dimensional Matrix-Variate Factor Models

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