Robust factor analysis for high-dimensional data with outliers

Outliers are commonly encountered in financial and economic data, and pose significant challenges to the study of the conventional factor models. This paper focuses on factor analysis for high-dimensional data in the presence of random outliers. We first propose a new class of factor model which incorporates a sparse outlier matrix. We then develop a class of robust methods to estimate the factor matrix and the number of factors. Under mild conditions, consistency of the proposed estimators is established. Judging from the numerical examples, we observe that the proposed estimation methods outperform existing approaches. Our methods significantly enhance the performance of the high-dimensional factor analysis when the data are contaminated by outliers.