Robust direction identification and variable selection in high dimensional general single-index models

Direction estimation and variable selection in a general class of models with single-index structure are considered. Under mild condition, we show simple linear quantile regression can offer a consistent and asymptotical normal estimate for the direction of index parameter vector in the presence of diverging number of predictors, and it does not need to estimate the link function, and without error distribution constraint. To do variable selection, we penalize the simple linear quantile regression by SCAD, and the oracle property is established. Simulation results and real data analysis confirm our method.