Sparse quantile regression

Le-Yu Chen and Sokbae (Simon) Lee

Journal of Econometrics, 2023, vol. 235, issue 2, 2195-2217

Abstract: We consider both ℓ0-penalized and ℓ0-constrained quantile regression estimators. For the ℓ0-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 ℓ0-constrained estimator. The resulting rates of convergence are nearly minimax-optimal and the same as those for ℓ1-penalized and non-convex penalized estimators. Further, we characterize expected Hamming loss for the ℓ0-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≈103 and up to p>103). In sum, our ℓ0-based method produces a much sparser estimator than the ℓ1-penalized and non-convex penalized approaches without compromising precision.

Keywords: Quantile regression; Sparse estimation; Mixed integer optimization; Finite sample property; Conformal prediction; Hamming distance (search for similar items in EconPapers)
JEL-codes: C21 C52 C61 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Related works:
Working Paper: Sparse Quantile Regression (2023)
Working Paper: Sparse Quantile Regression (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:235:y:2023:i:2:p:2195-2217

DOI: 10.1016/j.jeconom.2023.02.014

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