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<p>Matrix factor models have attracted increasing attention due to their advantage in achieving simultaneous two-way dimension reduction for matrix-structured observations. In this paper, we propose a new estimation method called Matrix Modified Huber Principal Component Analysis, which is robust against heavy-tailed errors. This approach applies the modified Huber loss function to the Frobenius norm of the idiosyncratic error matrix and performs principal component analysis on the weighted sample row and column covariance matrices, effectively estimating the loading and factor matrices. Furthermore, we design a data-driven procedure that adaptively chooses the tuning parameters to better accommodate the heavy-tailed nature of the data, and introduce a selection criterion based on an iterative eigenvalue ratio to estimate the number of factors. Simulation studies demonstrate that the proposed methods are superior or comparable to other existing methods in terms of robustness and accuracy. Finally, empirical analyses based on the Fama–French financial portfolio dataset and the multinational macroeconomic indices dataset validate the superiority of our methods.</p>

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Robust matrix factor analysis based on a modified huber loss function

  • 期刊论文

  • 发表日期：

    2026年4月11日

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  • Xinyu Yuan,
  • Fengkai Yang

摘要

Matrix factor models have attracted increasing attention due to their advantage in achieving simultaneous two-way dimension reduction for matrix-structured observations. In this paper, we propose a new estimation method called Matrix Modified Huber Principal Component Analysis, which is robust against heavy-tailed errors. This approach applies the modified Huber loss function to the Frobenius norm of the idiosyncratic error matrix and performs principal component analysis on the weighted sample row and column covariance matrices, effectively estimating the loading and factor matrices. Furthermore, we design a data-driven procedure that adaptively chooses the tuning parameters to better accommodate the heavy-tailed nature of the data, and introduce a selection criterion based on an iterative eigenvalue ratio to estimate the number of factors. Simulation studies demonstrate that the proposed methods are superior or comparable to other existing methods in terms of robustness and accuracy. Finally, empirical analyses based on the Fama–French financial portfolio dataset and the multinational macroeconomic indices dataset validate the superiority of our methods.