arXiv 27 Jan 2025 · Econometrics
arXiv:2501.15761 · PDF · DOI · OpenAlex · Extracted main text
We propose a new factor analysis framework and estimators of the factors and loadings that are robust to weak factors in a large $N$ and large $T$ setting. Our framework, by simultaneously considering all quantile levels of the outcome variable, induces standard mean and quantile factor models, but the factors can have an arbitrarily weak influence on the outcome's mean or quantile at most quantile levels. Our method estimates the factor space at the $\sqrt{N}$-rate without requiring the knowledge of weak factors' presence or strength, and achieves $\sqrt{N}$- and $\sqrt{T}$-asymptotic normality for the factors and loadings based on a novel sample splitting approach that handles incidental nuisance parameters. We also develop a weak-factor-robust estimator of the number of factors and consistent selectors of factors of any tolerated level of influence on the outcome's mean or quantiles. Monte Carlo simulations demonstrate the effectiveness of our method.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Bai, J (2003) Inferential theory for factor models of large dimensions | 1.000 | 13 | 6 | 100% |
| 2 | Bai, J. and S. Ng (2023) Approximate factor models with weaker loadings | 1.000 | 13 | 5 | 100% |
| 3 | Chen, L., J. J. Dolado, and J. Gonzalo (2021) Quantile factor models | 0.961 | 36 | 8 | 89% |
| 4 | Bai, J. and S. Ng (2002) Determining the number of factors in approximate factor models | 0.928 | 4 | 3 | 100% |
| 5 | Fernandes, M., E. Guerre, and E. Horta (2021) Smoothing quantile regressions | 0.894 | 7 | 5 | 71% |
| 6 | He, X., X. Pan, K. M. Tan, and W.-X. Zhou (2023) Smoothed quantile regression with large-scale inference | 0.811 | 4 | 2 | 100% |
| 7 | Fan, J., Y. Yan, and Y. Zheng (2024) When can weak latent factors be statistically inferred? | 0.737 | 3 | 2 | 100% |
| 8 | Onatski, A (2012) Asymptotics of the principal components estimator of large factor models with weakly influential factors | 0.737 | 3 | 2 | 100% |
| 9 | Galvao, A. F. and K. Kato (2016) Smoothed quantile regression for panel data | 0.644 | 3 | 2 | 67% |
| 10 | Bai, J. and S. Ng (2019) Rank regularized estimation of approximate factor models | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 34 scored citations.