Variable Selection for Nonparametric Quantile Regression via Smoothing Spline ANOVA

• Activity Number: 232
• Type: Topic Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Chen-Yen Lin*+ and Hao Helen Zhang and Howard Bondell and Hui Zou
• Companies: North Carolina State University and North Carolina State University and North Carolina State University and University of Minnesota
• Keywords: Quantile Regression ; Smoothing Spline ANOVA ; Model Selection

Abstract

Quantile regression provides a more thorough view of the effect of covariates on a response. In many cases, assuming a parametric form for the conditional quantile can be overly restrictive. Nonparametric quantile regression has recently become a viable alternative. The problem of variable selection for quantile regression is challenging, since important variables can influence various quantiles in different ways. We propose to tackle the problem using the approach of nonparametric quantile regression via regularization in the context of smoothing spline ANOVA models. By imposing the sum of the reproducing kernel Hilbert space norms on functions, the proposed sparse nonparametric quantile regression (SNQR) can identify variables which are important, and provide flexible nonparametric estimates for quantiles. We develop an efficient algorithm to solve the optimization problem and contribute an R package. Our numerical study suggests the promising performance of the new procedure in variable selection for nonparametric quantile regression.