Robust estimation for number of factors in high dimensional factor modeling via Spearman correlation matrix

TL;DR

This paper proposes a robust estimator for the number of factors in high-dimensional factor models using Spearman correlation, effective under heavy-tailed data and validated through theoretical consistency and numerical experiments.

Contribution

Introduces a novel Spearman correlation-based estimator for factor number that is robust to heavy tails in high-dimensional settings.

Findings

Estimator is consistent under mild conditions.

Outperforms existing methods in numerical experiments.

Robust against heavy-tailed data in factors and errors.

Abstract

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.