arXiv 19 Jun 2020 · Statistics — Methodology · publishedJournal of Econometrics (2023) · 7 citations (OpenAlex)
arXiv:2006.11201 · PDF · DOI · OpenAlex · Extracted main text
We consider both $\ell _{0}$-penalized and $\ell _{0}$-constrained quantile regression estimators. For the $\ell _{0}$-penalized estimator, we derive an exponential inequality on the tail probability of excess quantile prediction risk and apply it to obtain non-asymptotic upper bounds on the mean-square parameter and regression function estimation errors. We also derive analogous results for the $\ell _{0}$-constrained estimator. The resulting rates of convergence are nearly minimax-optimal and the same as those for $\ell _{1}$-penalized and non-convex penalized estimators. Further, we characterize expected Hamming loss for the $\ell _{0}$-penalized estimator. We implement the proposed procedure via mixed integer linear programming and also a more scalable first-order approximation algorithm. We illustrate the finite-sample performance of our approach in Monte Carlo experiments and its usefulness in a real data application concerning conformal prediction of infant birth weights (with $n\approx 10^{3}$ and up to $p>10^{3}$). In sum, our $\ell _{0}$-based method produces a much sparser estimator than the $\ell _{1}$-penalized and non-convex penalized approaches without compromising precision.
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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 | Belloni and Chernozhukov (2011) $_1$-penalized quantile regression in high-dimensional sparse models | 1.000 | 10 | 3 | 100% |
| 2 | Bertsimas, King, and Mazumder (2016) Best subset selection via a modern optimization lens | 0.965 | 10 | 4 | 90% |
| 3 | Wang (2019) $L_1$-regularized Quantile Regression with Many Regressors under Lean Assumptions | 0.874 | 8 | 2 | 100% |
| 4 | Wang, Wu, and Li (2012) Quantile Regression for Analyzing Heterogeneity in Ultra-High Dimension | 0.811 | 4 | 2 | 100% |
| 5 | Romano, Patterson, and Candes (2019) Conformalized quantile regression | 0.811 | 4 | 2 | 100% |
| 6 | Massart and Nédélec (2006) Risk bounds for statistical learning | 0.737 | 4 | 3 | 50% |
| 7 | Fan, Fan, and Barut (2014) Adaptive Robust Variable Selection | 0.737 | 3 | 2 | 100% |
| 8 | Huang, Jiao, Liu, and Lu (2018) A Constructive Approach to $L_0$ Penalized Regression | 0.737 | 3 | 2 | 100% |
| 9 | Wang and He (2022) Analysis of Global and Local Optima Of Regularized Quantile Regression in High Dimensions: A Subgradient Approach | 0.737 | 3 | 2 | 100% |
| 10 | Nesterov (2005) Smooth minimization of non-smooth functions | 0.644 | 4 | 1 | 100% |
Showing the top 10 of 44 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Fast Inference for Quantile Regression with Tens of Millions of Observations | 0.405 | 1 | 1 |