Robust Variable Selection Via Reciprocal Elastic Net in High-Dimensional Regression

Variable selection in high-dimensional regression models is crucial for improving interpretability and predictive accuracy. Traditional penalized ‎regression methods, such as the LASSO and Elastic Net, suffer from sensitivity to outliers, which can lead to biased coefficient estimation and ‎incorrect variable selection. In this study, we propose a robust variable selection method based on the reciprocal elastic net penalty, which ‎enhances sparsity while maintaining stability in the presence of extreme values. To further improve robustness, we integrate Huber loss and M-estimators, thereby mitigating the influence of outliers on the regression coefficients. The proposed method is evaluated through an extensive simulation ‎study under different contamination levels and applied to a financial risk dataset, where the presence of anomalies is common. Performance is ‎assessed using mean absolute error and breakdown point as evaluation criteria. The results demonstrate that the robust reciprocal elastic net ‎outperforms traditional penalized regression models and provides more reliable variable selection in the presence of outliers‎.