title: Variable Selection for Nonparametric Quantile Regression via Smoothing Spline AN OVA.
abstract: Quantile regression provides a more thorough view of the effect of covariates on a response. Nonparametric quantile regression has become a viable alternative to avoid restrictive parametric assumption. The problem of variable selection for quantile regression is challenging, since important variables can influence various quantiles in different ways. We tackle the problem via regularization in the context of smoothing spline ANOVA models. The proposed sparse nonparametric quantile regression (SNQR) can identify important variables and provide flexible estimates for quantiles. Our numerical study suggests the promising performance of the new procedure in variable selection and function estimation. Supplementary materials for this article are available online.
authors.affiliation: Eli Lilly and Company, IN 46285.
authors.forename: Chen-Yen
authors.initials: CY
authors.lastname: Lin
authors.affiliation: Department of Statistics, North Carolina State University, NC 27695-8203.
authors.forename: Howard
authors.initials: H
authors.lastname: Bondell
authors.affiliation: Department of Mathematics, University of Arizona, AZ 85721-0089.
authors.forename: Hao Helen
authors.initials: HH
authors.lastname: Zhang
authors.affiliation: School of Statistics, University of Minnesota, MN 55455.
authors.forename: Hui
authors.initials: H
authors.lastname: Zou
keywords: COSSO; Kernel Quantile Regression; Model Selection; Reproducing Kernel Hilbert Space