Arbeitspapier
Sparse quantile regression
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 minimax-optimal and the same as those for l1-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 ≈ 10 to the 3rd and up to p > 10 to the 3rd ). In sum, our l0-based method produces a much sparser estimator than the l1-penalized approach without compromising precision.
- Language
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Englisch
- Bibliographic citation
-
Series: cemmap working paper ; No. CWP30/20
- Classification
-
Wirtschaft
- Subject
-
quantile regression
sparse estimation
mixed integer optimization
finitesample property
conformal prediction
Hamming distance
- Event
-
Geistige Schöpfung
- (who)
-
Chen, Le-Yu
Lee, Sokbae
- Event
-
Veröffentlichung
- (who)
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Centre for Microdata Methods and Practice (cemmap)
- (where)
-
London
- (when)
-
2020
- DOI
-
doi:10.1920/wp.cem.2020.3020
- Handle
- Last update
-
20.09.2024, 8:22 AM CEST
Data provider
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Arbeitspapier
Associated
- Chen, Le-Yu
- Lee, Sokbae
- Centre for Microdata Methods and Practice (cemmap)
Time of origin
- 2020
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