Robust regression: Testing global hypotheses about the slopes when there is multicollinearity or heteroscedasticity

Area of Science:

• Statistics
• Econometrics
• Data Science

Background:

• Multicollinearity in linear regression inflates standard errors, reducing statistical power.
• Outliers in dependent and independent variables (leverage points) further complicate regression analysis.

Purpose of the Study:

• To develop a robust heteroscedastic method for handling multicollinearity.
• To improve hypothesis testing power for slope parameters in the presence of multicollinearity and outliers.

Main Methods:

• Utilizing a robust ridge estimator designed to be resilient to outliers.
• Examining heteroscedasticity and its impact on regression estimators.
• Incorporating analysis of leverage points (outliers in independent variables).

Main Results:

• The proposed robust ridge estimator effectively mitigates multicollinearity issues.
• The method demonstrates substantial power increases in hypothesis testing across various scenarios.
• The approach provides robustness against both dependent variable outliers and leverage points.

Conclusions:

• The developed heteroscedastic robust ridge estimator offers a powerful solution for multicollinearity.
• This method enhances the reliability of linear regression models in the presence of data anomalies.
• It provides a valuable tool for researchers dealing with complex, real-world datasets.