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CAN PRINCIPAL COMPONENT ANALYSIS PRESERVE THE SPARSITY IN FACTOR LOADINGS?

J. Wei & Yonghui Zhang

Econometric Theory2026https://doi.org/10.1017/s0266466625100303article
AJG 4ABDC A*
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0.50

Abstract

This article studies the principal component analysis (PCA) estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PCA estimators of loadings, which comes from the approximately (block) upper triangular structure of the rotation matrix. It suggests an asymmetric relationship among factors: the sparsity of the rotated loadings for a stronger factor can be contaminated by the loadings from weaker ones, but the sparsity of the rotated loadings of a weaker factor is almost unaffected by the loadings of stronger ones. Then, we propose a simple alternative to the existing penalized approaches to sparsify the loading estimators by screening out the small PCA loading estimators directly, and construct consistent estimators for factor strengths. The proposed estimators perform well in finite samples, as shown by a set of Monte Carlo simulations.

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https://doi.org/https://doi.org/10.1017/s0266466625100303

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@article{j.2026,
  title        = {{CAN PRINCIPAL COMPONENT ANALYSIS PRESERVE THE SPARSITY IN FACTOR LOADINGS?}},
  author       = {J. Wei & Yonghui Zhang},
  journal      = {Econometric Theory},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1017/s0266466625100303},
}

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0.50

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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