Alexandre Belloni, Mingli Chen, Oscar Hernan Madrid Padilla, Zixuan, Wang
arXiv 4 Dec 2019 · Econometrics · publishedThe Annals of Statistics (2023) · 9 citations (OpenAlex)
arXiv:1912.02151 · PDF · DOI · OpenAlex · Extracted main text
We propose a generalization of the linear panel quantile regression model to accommodate both sparse and dense parts: sparse means while the number of covariates available is large, potentially only a much smaller number of them have a nonzero impact on each conditional quantile of the response variable; while the dense part is represent by a low-rank matrix that can be approximated by latent factors and their loadings. Such a structure poses problems for traditional sparse estimators, such as the $\ell_1$-penalised Quantile Regression, and for traditional latent factor estimator, such as PCA. We propose a new estimation procedure, based on the ADMM algorithm, consists of combining the quantile loss function with $\ell_1$ and nuclear norm regularization. We show, under general conditions, that our estimator can consistently estimate both the nonzero coefficients of the covariates and the latent low-rank matrix. Our proposed model has a "Characteristics + Latent Factors" Asset Pricing Model interpretation: we apply our model and estimator with a large-dimensional panel of financial data and find that (i) characteristics have sparser predictive power once latent factors were controlled (ii) the factors and coefficients at upper and lower quantiles are different from the median.
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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 | barticle[author] Belloni, AlexandreA. Chernozhukov, VictorV (2011) ) | 1.000 | 28 | 4 | 100% |
| 2 | barticle[author] Yu, BinB (1994) ) | 1.000 | 9 | 4 | 100% |
| 3 | barticle[author] Boyd, StephenS., Parikh, NealN., Chu, EricE., Pelea… (2011) ) | 1.000 | 5 | 3 | 100% |
| 4 | barticle[author] Padilla, Oscar Hernan MadridO. H. M. Chatterjee, Sa… (2020) ) | 0.928 | 4 | 3 | 100% |
| 5 | barticle[author] Moon, Hyungsik RogerH. R. Weidner, MartinM (2018) ) | 0.874 | 6 | 2 | 100% |
| 6 | barticle[author] Daniel, KentK. Titman, SheridanS (1997) ) | 0.874 | 5 | 2 | 100% |
| 7 | barticle[author] Chatterjee, SouravS (2015) ) | 0.843 | 3 | 3 | 100% |
| 8 | barticle[author] Elsener, AndreasA. van de Geer, SaraS (2018) ) | 0.843 | 3 | 3 | 100% |
| 9 | bbook[author] van der Vaart, Aad W.A. W. Wellner, Jon AJ. A (1996) ) | 0.843 | 3 | 3 | 100% |
| 10 | barticle[author] Daniel, KentK. Titman, SheridanS (1998) ) | 0.811 | 4 | 2 | 100% |
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