Robust projected principal component analysis for large-dimensional semiparametric factor modeling

作者：Yang, Shuquan; Ling, Nengxiang^*

来源：Journal of Multivariate Analysis, 2023, 195: 105155.

DOI：10.1016/j.jmva.2023.105155

• Huber regression
• Panel data models
• Robust estimation
• Semiparametric factor models

Semiparametric factor structures are ubiquitous in panel data analysis. Conventional methods for estimating the regression coefficients based on the least-squares principle suffer from the shortcoming of non-robustness. In this paper, we introduce the Huber regression into panel data models with a semiparametric factor structure. To estimate the regression coefficients robustly, we apply the projected principal component analysis method to recover the factors and nonparametric loadings. The Huber estimator and the penalized Huber estimator of the regression coefficients are obtained through iterative optimization procedures, where both factors and idiosyncratic errors are allowed to be heavy-tailed and serially-correlated. Moreover, we establish the non-asymptotic properties of the estimated factors, loadings, and regression coefficients under some mild conditions. Extensive simulations and a real data analysis have been carried out to support our theories.