Quantile-based robust ridge m-estimator for linear regression model in presence of multicollinearity and outliers

Abstract

In linear regression model, the ordinary least square and ridge regression estimators are sensitive to outliers in y-direction. In this article, we proposed two new robust quantile-based ridge and ridge m-estimators (QR and QRM) to deal with multicollinearity and outliers in y-direction. A simulation study has been conducted to compare the performance of the estimators. Based on mean square error criterion, it is shown that QR and QRM estimators outperform other considered estimators in many evaluated instances. An application is given to illustrate the performance of proposed estimators.

Keywords:

• Multicollinearity
• m-estimator
• MSE
• outliers
• ridge regression

Acknowledgments

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

Additional information

Funding

Higher Education Commission Pakistan (https://www.hec.gov.pk) Indigenous PhD fellowship Phase-II Batch-III under grant no: 315-11394-2PS3-084 awarded to the first author.