Robust Estimation for Number of Factors in High Dimensional Factor Modeling via Spearman Correlation Matrix

Abstract

Determining the number of factors in high-dimensional factor modeling is essential but challenging, especially when the data are heavy-tailed. In this article, 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. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.