Estimation and variable selection for a class of quantile regression models with multiple index

Quantile regression (QR) for a groupwise additive multiple-index models and its applications are investigated. We find that quantile regression can be used to recovery the directions of the index parameter vectors, and it does not involve the nonparametric treatment completely. Based on this useful finding, a iterative-free QR estimator for the partial linear single index model and a penalized QR for variable selection in the high dimensional sparse models are proposed respectively. Because of inheriting the superiorities of quantile regression, our methods are robust and comprehensive. Simulation studies and real data analysis are included to illustrate the finite sample performance.