An elastic-net penalized expectile regression with applications

Abstract

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.

Keywords:

• Expectile regression
• elastic-net
• SNCD
• variable selection
• high-dimensional data

Classification codes:

• 62J05

Acknowledgments

The authors are grateful to the Editor-in-Chief, the associated Editor, and three anonymous referees for their helpful comments and constructive guidance. This work was supported by the National Natural Science Foundation of China (71671056), the Humanity and Social Science Foundation of the Ministry of Education of China (19YJA790035), the Nature Science Foundation in the Universities of Anhui Province (XJ2019000103, KJ2017A391), and the National Statistical Science Research Projects of China (2019LD05).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (71671056), the Humanity and Social Science Foundation of the Ministry of Education of China (19YJA790035), the Nature Science Foundation in the Universities of Anhui Province (XJ2019000103, KJ2017A391), and the National Statistical Science Research Projects of China (2019LD05).