A1064
Title: Sparse quantile regression
Authors: Le-Yu Chen - Institute of Economics, Academia Sinica (Taiwan) [presenting]
Sokbae Lee - Columbia University (United States)
Abstract: Both L0-penalized and L0-constrained quantile regression estimators are considered. For the L0-penalized estimator, an exponential inequality on the tail probability of excess quantile prediction risk is derived, and it is applied to obtain non-asymptotic upper bounds on the mean-square parameter and regression function estimation errors. Analogous results for the L0-constrained estimator are also derived. The resulting rates of convergence are nearly minimax-optimal, and the same as those for L1-penalized and non-convex penalized estimators. Further, the expected Hamming loss for the L0-penalized estimator is characterized. The proposed procedure is implemented via mixed integer linear programming and also a more scalable first-order approximation algorithm. The finite-sample performance of the proposed approach in Monte Carlo experiments and its usefulness in a real data application concerning the conformal prediction of infant birth weights (with n ~ 1000 and up to p>1000) are illustrated. In sum, the L0-based method produces a much sparser estimator than the L1-penalized, and non-convex penalized approaches without compromising precision.
