Single-index composite quantile regression for ultra-high-dimensional data

Composite quantile regression (CQR) is a robust and efficient estimation method. This paper studies CQR method for single-index models with ultra-high-dimensional data. We propose a penalized CQR estimator for single-index models and combine the debiasing technique with the CQR method to construct an estimator that is asymptotically normal, which enables the construction of valid confidence intervals and hypothesis testing. Both simulations and data analysis are conducted to illustrate the finite sample performance of the proposed methods.