Abstract In this paper, we investigate the robust estimation of the number of common factors in high-dimensional factor model with pair-elliptically distributed idiosyncratic errors. Motivated by the pandemic heavy-tail distributions of financial returns, we first introduce a pair-elliptical factor model by allowing the factors and noises to follow pairwisely the joint elliptical distributions. Compared with the elliptical factor model invented in Fan et al. (Ann Stat 46:1383–1414, 2018), the pair-elliptical factor model has more richer structure with more relaxed assumptions. We propose two robust quantile-based estimators of the number of factors and obtain the asymptotic properties of the estimators under some mild conditions. Then, some simulation studies and a real data analysis are carried out to show the effectiveness of the estimators of the factor numbers.
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机译：摘要 研究了具有成对椭圆分布特异质误差的高维因子模型中公因子数的鲁棒估计方法。受疫情重尾效应影响，我们首先引入成对椭圆因子模型，让因子和噪声成对跟随联合椭圆分布。与Fan等人（Ann Stat 46：1383–1414， 2018）发明的椭圆因子模型相比，椭圆因子对模型结构更丰富，假设更宽松。我们提出了两种基于分位数的因子数的鲁棒估计器，并获得了估计器在一些温和条件下的渐近性质。然后，通过仿真研究和实际数据分析，验证了因子数估计器的有效性。
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