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

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.

Automated summary

Two new robust quantile-based ridge estimators, QR and QRM, are proposed in this article to deal with outliers and multicollinearity in linear regression models. A simulation study shows that these estimators outperform other considered estimators based on mean square error criterion. An application is provided to demonstrate the performance of the proposed estimators.