One-step group factor analysis via penalized least squares
Abstract
In this article, we revisit the problem of group factor analysis and propose a one-step penalized least squares method to estimate the factor loadings and factors in large-dimensional group factor models, offering a distinct alternative to the conventional two-step principal component approach. Our procedure originates from the equivalence between the group factor structure and the carefully tailored identification conditions. Leveraging this insight, we develop a tricky Lagrange multiplier formulation for a penalized least square loss function. This one-step optimization framework, combined with the fine-tuned penalty parameters, facilitates the direct derivation of central limit theorems for factor loadings, factor scores, common and local components, as well as the convergence rates for them. Our theory demonstrates that our one-step approach achieves the same rate as the two-step aggregated principal-component method and even the same limiting standard error in the balanced group panel case, but smaller limiting standard error than the two-step canonical correlation procedure. Extensive simulation studies justify the theory. Applications to U.S. house prices and CSI300 weekly returns confirm that our method identifies global factors and heterogeneous local patterns.
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BibTeX
@misc{kong2026onestep,
title = {{One-step group factor analysis via penalized least squares}},
author = {Xinbing Kong and Xiaoying Pan and Long Yu and Tong Zhang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29625},
eprint = {2608.29625},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29625},
}
RIS
TY - UNPB
TI - One-step group factor analysis via penalized least squares
AU - Xinbing Kong
AU - Xiaoying Pan
AU - Long Yu
AU - Tong Zhang
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29625
UR - https://arxiv.org/abs/2608.29625
AB - In this article, we revisit the problem of group factor analysis and propose a one-step penalized least squares method to estimate the factor loadings and factors in large-dimensional group factor models, offering a distinct alternative to the conventional two-step principal component approach. Our procedure originates from the equivalence between the group factor structure and the carefully tailored identification conditions. Leveraging this insight, we develop a tricky Lagrange multiplier formulation for a penalized least square loss function. This one-step optimization framework, combined with the fine-tuned penalty parameters, facilitates the direct derivation of central limit theorems for factor loadings, factor scores, common and local components, as well as the convergence rates for them. Our theory demonstrates that our one-step approach achieves the same rate as the two-step aggregated principal-component method and even the same limiting standard error in the balanced group panel case, but smaller limiting standard error than the two-step canonical correlation procedure. Extensive simulation studies justify the theory. Applications to U.S. house prices and CSI300 weekly returns confirm that our method identifies global factors and heterogeneous local patterns.
ER -