Variable selection for non-parametric quantile regression via smoothing spline analysis of variance

Quantile regression provides a more thorough view of the effect of covariates on a response. Non-parametric quantile regression has become a viable alternative to avoid restrictive parametric assumption. The problem of variable selection for quantile regression is challenging, as important variables can influence various quantiles in different ways. We tackle the problem via regularization in the context of smoothing spline analysis of variance models. The proposed sparse non-parametric quantile regression 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.