Non-crossing quantile regression via doubly penalized kernel machine

Quantile regression provides a more complete statistical analysis of the stochastic relationships among random variables. Sometimes quantile regression functions estimated at different orders can cross each other. We propose a new non-crossing quantile regression method using doubly penalized kernel machine (DPKM) which uses heteroscedastic location-scale model as basic model and estimates both location and scale functions simultaneously by kernel machines. The DPKM provides the satisfying solution to estimating non-crossing quantile regression functions when multiple quantiles for high-dimensional data are needed. We also present the model selection method that employs cross validation techniques for choosing the parameters which affect the performance of the DPKM. One real example and two synthetic examples are provided to show the usefulness of the DPKM.