Novel Robust Estimators for the Linear Regression Model with Multicollinearity and Outlier Problems

Abstract

In this study, we introduce new robust M estimators based on ridge estimation (M-Ridge) for data sets with both multicollinearity and outlier problems in multiple linear regression analysis. In the proposed approach, the iterative re-weighted least squares (IRLS) algorithm for parameter estimation is implemented based on ridge estimation.The proposed approach also provides a solution to the problem of the optimal ridge estimator selection with M-type estimators. The performance of the proposed estimators is evaluated against other estimators using a Monte Carlo simulation study and a real data application. The estimated mean square error (MSE) and k-fold cross validation are used as performance measures in the Monte Carlo simulation study and the real data application, respectively. The proposed M-Ridge estimators outperformed the other estimators considered in many evaluated instances in both the simulation study and the real data application.