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.

翻译：矩阵因子模型因能对结构良好的矩阵观测数据同时进行双向降维而日益受到关注。本文聚焦于“维度发散”框架下矩阵因子模型的稳健统计推断。在 idiosyncratic 误差仅具有有限二阶矩的假设下，我们推导了因子载荷、因子及共同成分的稳健估计量的收敛速率。此外，在温和条件下还推导了这些估计量的渐近分布。我们提出了一种秩最小化方法与一种特征值比值方法，以一致地估计因子对个数。数值实验证实，迭代Huber回归算法是估计矩阵因子模型的一种实用且可靠的方法，尤其在具有重尾 idiosyncratic 误差的情形下。我们通过两个真实数据集（一个涵盖金融投资组合，另一个涉及中国宏观经济指数）展示了所提方法的实际应用价值。