Huber Principal Component Analysis for large-dimensional factor models

Yong He, Lingxiao Li, Dong Liu and Wen-Xin Zhou

Journal of Econometrics, 2025, vol. 249, issue PB

Abstract: Factor models have been widely used in economics and finance. However, the heavy-tailed nature of macroeconomic and financial data is often neglected in statistical analysis. To address this issue, we propose a robust approach to estimate factor loadings and scores by minimizing the Huber loss function, which is motivated by the equivalence between conventional Principal Component Analysis (PCA) and the constrained least squares method in the factor model. We provide two algorithms that use different penalty forms. The first algorithm involves an element-wise-type Huber loss minimization, solved by an iterative Huber regression algorithm. The second algorithm, which we refer to as Huber PCA, minimizes the ℓ2-norm-type Huber loss and performs PCA on the weighted sample covariance matrix. We examine the theoretical minimizer of the element-wise Huber loss function and demonstrate that it has the same convergence rate as conventional PCA when the idiosyncratic errors have bounded second moments. We also derive their asymptotic distributions under mild conditions. Moreover, we suggest a consistent model selection criterion that relies on rank minimization to estimate the number of factors robustly. We showcase the benefits of the proposed two algorithms through extensive numerical experiments and a real macroeconomic data example. An R package named “HDRFA” 11https://cran.r-project.org/web/packages/HDRFA/index.html. has been developed to conduct the proposed robust factor analysis.

Keywords: Factor model; Heavy-tailed data; Huber loss; Principal component analysis; Rank minimization (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304407625000478
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:249:y:2025:i:pb:s0304407625000478

DOI: 10.1016/j.jeconom.2025.105993

Access Statistics for this article

Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

More articles in Journal of Econometrics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().