Expectile regression is a flexible statistical modeling approach widely used in econometrics, medicine, and high-dimensional data analysis. However, a significant challenge in constructing expectile regression models is the accurate selection of active covariates, especially in the presence of multicollinearity. While traditional penalized regression techniques, such as SCAD and Elastic Net, provide solutions, they often face limitations in variable selection stability and predictive accuracy.
In this study, we propose Expectile Regression with Adaptive Elastic Net penalty (ER-AdEN), a novel method that integrates Lasso and Ridge penalties with adaptive weighting to enhance variable selection and address multicollinearity. The adaptive weights are designed to improve the stability of variable selection, particularly in high-dimensional settings. The proposed method is evaluated through extensive Monte Carlo simulations and a real-world application involving diabetes prediction. Performance is compared against ER-SCAD and ER-Elastic Net using key evaluation metrics, including Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Expected Prediction Error (EPE).
Simulation results demonstrate that ER-AdEN consistently outperforms competing methods in terms of predictive accuracy, robustness, and sparsity control. For instance, in scenarios with Gaussian errors, ER-AdEN achieved an RMSE of 0.210 compared to 0.235 for ER-SCAD and 0.245 for ER-Elastic Net. In the real data analysis, ER-AdEN achieves superior variable selection efficiency and lower prediction error when applied to diabetes data, reducing the prediction error by approximately 15% compared to traditional methods. These results highlight the potential of ER-AdEN as a reliable tool for high-dimensional regression problems, particularly in medical data analysis.
International Journal of Statistics and Applied Mathematics
