Gini-weighted class of ridge estimators in linear regression with heteroscedastic errors

Abstract

The joint presence of multicollinearity and heteroscedasticity substantially deteriorates the performance of ordinary least squares and ridge estimators. To address this, a robust heteroscedasticity-adjusted ridge estimator is proposed that incorporates a data-dependent scaling factor based on the Gini index. The proposed scaling factor is integrated into the traditional ridge parameter to mitigate unjust penalization arising due to heteroscedasticity and severe multicollinearity. Monte Carlo simulation across varying sample sizes, dimensionalities, multicollinearity levels, and degrees of heteroscedasticity shows a substantial reduction in mean squared error, with the most notable improvements observed in scenarios where predictors are highly correlated and error variances exhibit extreme heteroscedasticity. Further, the proposed methodology is applied to the Auto-MPG and Pakistan Economic datasets, which demonstrate the challenging characteristics addressed in this study. The PRESS confirms that the Gini-adjusted ridge parameter achieves superior predictive accuracy and more stable coefficient estimates compared to existing approaches.

Keywords

• Gini index
• heteroscedasticity
• multicollinearity
• ridge regression
• scaling factor

References

1. [1] A. A. Al-Majali, The effect of democracy and income inequality (Gini index), Jordan. J. Law Polit. Sci. 15 (4), 2023.