Determining the number of factors in high-dimensional factor modeling is essential but challenging, especially when the data are heavy-tailed. In this paper, we introduce a new estimator based on the spectral properties of Spearman sample correlation matrix under the high-dimensional setting, where both dimension and sample size tend to infinity proportionally. Our estimator is robust against heavy tails in either the common factors or idiosyncratic errors. The consistency of our estimator is established under mild conditions. Numerical experiments demonstrate the superiority of our estimator compared to existing methods.

翻译：在高维因子模型中确定因子数量至关重要但具有挑战性，尤其在数据存在重尾特征时。本文提出一种基于斯皮尔曼样本相关矩阵谱性质的新估计量，适用于维度与样本量成比例趋于无穷的高维场景。该估计量对公共因子或特质误差中的重尾分布具有稳健性，并在温和条件下证明了其相合性。数值实验表明，该估计量相较现有方法具有显著优越性。