Statistical Inference for High-Dimensional Matrix-Variate Factor Model
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This paper considers the estimation and inference of factor loadings, latent factors and the low-rank components in high-dimensional matrix-variate factor model, where each dimension of the matrix-variates (p × q) is comparable to or greater than the number of observations (T). We preserve matrix structure in the estimation and develop an inferential theory, establishing consistency, the rate of convergence, and the limiting distributions. We show that the estimated loading matrices are asymptotically normal. These results are obtained under general conditions that allow for correlations across time, rows or columns of the noise. Stronger results are obtained when the noise is temporally, row- and/or column-wise uncorrelated. Simulation results demonstrate the adequacy of the asymptotic results in approximating the finite sample properties. Our proposed method compares favorably with the existing methods. We illustrate the proposed model and estimation procedure with a real numeric data set and a real image data set. In both applications, the proposed estimation procedure outperforms previous methods in the power of variance explanation under the out-of-sample 10-fold cross-validation setting.
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