Abstract

 Robust variable selection is essential in high-dimensional medical data analysis, where the presence of outliers can significantly impact model performance. This study introduces the Reciprocal Lasso, a novel regularization method that enhances robustness while preserving sparsity in regression modeling. The method incorporates an inverse penalty function that dynamically adjusts the penalization strength based on coefficient magnitudes, reducing sensitivity to extreme values. 
A comprehensive simulation study is conducted to evaluate the performance of the Reciprocal Lasso under varying levels of contamination, comparing it to the Adaptive Lasso and the S-Estimator-based Lasso. To further improve robustness, the model is integrated with Tukey’s Biweight Loss Function and MM-Estimators, which provide stronger resistance against extreme observations and improve estimation stability. The results demonstrate that the Reciprocal Lasso achieves superior variable selection accuracy, lower prediction error, and greater stability in the presence of outliers. Additionally, the method is applied to a real-world medical dataset, where it effectively identifies relevant biomarkers associated with disease progression while maintaining robustness to data anomalies. These findings suggest that the Reciprocal Lasso, combined with advanced robust estimation techniques, is a promising approach for high-dimensional modeling in medical research. Future studies could explore its application in genomic and epidemiological studies, as well as its integration with Bayesian frameworks for uncertainty quantification.