Heteroscedastic-adjusted standard error based estimation of ridge parameter in the linear regression model

In this study, we revisit the estimation problem in linear regression under the simultaneous presence of multicollinearity and heteroscedasticity. Under this situation, the performance of classical ordinary least squares (OLS) and ridge estimators deteriorates significantly. To address these challenges, a class of heteroscedastic ridge estimators is introduced. The new estimators are based on the heteroscedastic-adjusted standard error, which is the positive root of a scaling factor and OLS error variance. Extensive simulations are conducted to assess the performance of suggested estimators in terms of mean squared error (MSE). The findings demonstrate that the suggested heteroscedastic-adjusted ridge estimators (HAREs) outperform their counterparts, particularly when high collinearity exists among regressors across different levels of heteroscedasticity (low, high, and severe). Additionally, the performance of the HAREs is compared with existing estimators under similar scenarios. A real-life data application further highlights the utility of the suggested HAREs when regressors are highly correlated, and the error term deviates from homoscedasticity.