ABSTRACT In the recent studies, a condition index based biasing parameter ‘ k ’ has been introduced by Dar et al. (2023) to overcome the problem of multicollinearity in ridge regression setting. The introduced estimator has better properties than conventional ridge regression estimators. However, the presence of outliers in the data set may have some adverse effects on the condition index base estimator. To overcome such limitation, we modify the Dar estimator by taking the range of the eigen values of the correlation matrix instead of condition index and introduce three new range based robust estimators. An extensive simulation study is made through mean squared error evaluation metric to compare the performance of estimators. The simulation results show that new estimators outperform in many evaluated instances. We include three numerical examples to see the predictive accuracy of new estimators via prediction error sum of squares evaluation criteria. The applications support the simulation findings and show the best performance of new estimators to overcome the joint problem of multicollinearity and outliers.
Khan et al. (Wed,) studied this question.