Robust Regression Estimation: A Doubly Weighted M-Estimation Approach with Generalized Jackknife Resampling

Robust regression estimation is crucial in addressing the influence of outliers and model misspecification in statistical modelling. This study proposes a Doubly Weighted M-Estimation (DWME) approach, integrating an adaptive weighting scheme with Generalized Jackknife Resampling (GJR) to enhance efficiency and robustness in parameter estimation. The DWME method incorporates case-specific and parameter-specific weighting functions, ensuring resistance against leverage points and heavy-tailed distributions. By leveraging GJR, the proposed estimator achieves reduced bias and variance while maintaining asymptotic efficiency under mild regularity conditions. Empirical analyses demonstrate that DWME outperforms traditional M-estimators, Least Absolute Deviation (LAD), and Huber regression in terms of robustness, efficiency, and predictive accuracy. The proposed methodology offers a reliable alternative for robust estimation in heteroscedastic, non-normal, and contaminated datasets, making it particularly valuable for econometric and high-dimensional applications.