Two-step ridge framework to handle heteroscedasticity and multicollinearity in linear regression model: a data-driven shrinkage approach

Reliable parameter estimation in linear regression becomes particularly challenging in the presence of highly correlated predictors and heteroscedastic errors. To address these issues, this study offers a two-step weighted ridge regression estimation (TS-WRE) framework specifically designed for such situations. The performance of the proposed TS-WRE method is evaluated through Monte Carlo simulations using synthetic data across multiple scenarios. The simulation-based mean squared error (MSE) results indicate that the proposed estimators generally outperform existing approaches under moderate-to-severe multicollinearity and heteroscedasticity, while remaining competitive in other scenarios. In addition, the practical applicability of the TS-WRE is illustrated using China’s economic growth data and livestock data, highlighting the usefulness of the proposed method.