Combining principal component and robust ridge estimators in linear regression model with multicollinearity and outlier

The method of least squared suffers a setback when there is multicollinearity and outliers in the linear regression model. In this article, we developed a new estimator to jointly handle multicollinearity and outliers by pooling the following estimators together: the M-estimator, the principal component and the ridge estimator. The new estimator is called the robust r-k estimator and is employed. We established theoretically that the new estimator is better than some of the existing ones. The simulation studies and real-life application supports the efficiency of the new method.