Robust estimation of the number of factors for the pair-elliptical factor models

作者：Yang, Shuquan; Ling, Nengxiang^*; Gong, Yulin

来源：COMPUTATIONAL STATISTICS, 2022, 37(3): 1495-1522.

DOI：10.1007/s00180-021-01165-5

• Pair-elliptical factor model
• Static approximate factor model
• Robust estimation
• Quantile

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.