An elastic-net penalized expectile regression with applications.

To perform variable selection in expectile regression, we introduce the elastic-net penalty into expectile regression and propose an elastic-net penalized expectile regression (ER-EN) model. We then adopt the semismooth Newton coordinate descent (SNCD) algorithm to solve the proposed ER-EN model in high-dimensional settings. The advantages of ER-EN model are illustrated via extensive Monte Carlo simulations. The numerical results show that the ER-EN model outperforms the elastic-net penalized least squares regression (LSR-EN), the elastic-net penalized Huber regression (HR-EN), the elastic-net penalized quantile regression (QR-EN) and conventional expectile regression (ER) in terms of variable selection and predictive ability, especially for asymmetric distributions. We also apply the ER-EN model to two real-world applications: relative location of CT slices on the axial axis and metabolism of tacrolimus (Tac) drug. Empirical results also demonstrate the superiority of the ER-EN model.