Xu Q F, Ding X H, Jiang C X, Yu K M, Shi L
School of Management, Hefei University of Technology, Hefei, People's Republic of China.
Key Laboratory of Process Optimization and Intelligent Decision-making, Ministry of Education, Hefei, People's Republic of China.
J Appl Stat. 2020 Jun 30;48(12):2205-2230. doi: 10.1080/02664763.2020.1787355. eCollection 2021.
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.
为了在期望分位数回归中进行变量选择，我们将弹性网罚项引入期望分位数回归，并提出了一种弹性网罚期望分位数回归（ER - EN）模型。然后，我们采用半光滑牛顿坐标下降（SNCD）算法在高维设置下求解所提出的ER - EN模型。通过广泛的蒙特卡罗模拟说明了ER - EN模型的优势。数值结果表明，在变量选择和预测能力方面，尤其是对于非对称分布，ER - EN模型优于弹性网罚最小二乘回归（LSR - EN）、弹性网罚Huber回归（HR - EN）、弹性网罚分位数回归（QR - EN）和传统期望分位数回归（ER）。我们还将ER - EN模型应用于两个实际应用：CT切片在轴向上的相对位置和他克莫司（Tac）药物的代谢。实证结果也证明了ER - EN模型的优越性。
