Estimation And Variable Selection For The Single Index Quantile Regression Model

Single index model is a kind of flexible semiparametric model and it is widely used.This paper we will use the B-spline smoothing technique and quantile regression method to research the estimates and variable selection problem of single index model.Firstly,B spline smoothing technique is used to approximate the unknown index function.Then we get the index function estimate by the nonlinear optimization method based on port.We propose a variable selection procedure for the QR of SIM by the adaptive LASSO penalized method to get sparse estimation of the index parameter.Through simulation studies,we illustrate the performance of our proposed method.We also extend the variable selection approach on the SIM and further study the variable selection on the QR of PLSIM.