Matrix factor model is drawing growing attention for simultaneous two-way
dimension reduction of well-structured matrix-valued observations. This paper
focuses on robust statistical inference for matrix factor model in the
``diverging dimension" regime. We derive the convergence rates of the robust
estimators for loadings, factors and common components under finite second
moment assumption of the idiosyncratic errors. In addition, the asymptotic
distributions of the estimators are also derived under mild conditions. We
propose a rank minimization and an eigenvalue-ratio method to estimate the pair
of factor numbers consistently. Numerical studies confirm the iterative Huber
regression algorithm is a practical and reliable approach for the estimation of
matrix factor model, especially under the cases with heavy-tailed idiosyncratic
errors . We illustrate the practical usefulness of the proposed methods by two
real datasets, one on financial portfolios and one on the macroeconomic indices
of China