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

Abstract 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.