Pure Mathematics for Theoretical Computer Science

This study investigates the effectiveness of variable selection techniques in linear regression models under grouped structures and correlation among predictors. Specifically, it evaluates and compares the performance of three prominent methods: LASSO, Elastic Net, and OSCAR. The simulation study spans multiple scenarios, including varying correlation levels and sample sizes, and utilizes key metrics such as Mean Squared Error (MSE), True Positive Rate (TPR), False Positive Rate (FPR), and Grouping Accuracy. The results reveal the superior performance of OSCAR, particularly in grouped settings, where it consistently achieves lower error rates and better variable selection accuracy. A real data application using the prostate cancer dataset further supports the empirical advantages of OSCAR over its counterparts, especially in scenarios involving correlated and grouped predictors. The findings provide strong evidence in favor of OSCAR as a reliable tool for robust regression modeling.