Bagging-based ridge estimators for a linear regression model with non-normal and heteroscedastic errors

Abstract

Regression analysis is used to predict a dependent variable using one or more independent variables. In the linear regression model, when the independent variables are highly correlated, it leads toward the problem of multicollinearity. Subsequently, the ordinary least squares estimates become inconsistent and may lead to wrong inferences. In such a situation, ridge regression is the most commonly adopted technique. In this paper, we propose some new bootstrap aggregation (bagging) based ridge estimators. The performance of the proposed estimators is evaluated by a simulation study in terms of minimum mean squared error. The simulation results indicate that in the presence of multicollinearity with non-normal or heteroscedastic errors, the bagging-based ridge estimators perform better than conventional ridge estimators. The estimation of biasing parameters using bagging approach promotes the performance of the conventional ridge estimators. Finally, the real-life example is used to demonstrate the application of proposed estimators.

Keywords:

• Multicollinearity
• Non-normal
• Bagging
• Ridge estimators
• Heteroscedastic

Acknowledgements

Authors are thankful to the referees for their valuable comments and suggestions, which certainly improved the presentation and quality of the article.