A Comparative Study between Ridge MM and Ridge Least Trimmed Squares Estimators in Handling Multicollinearity and Outliers

Abstract

Common problems found in multiple linear regression models are the existence of multicollinearity and outliers. These obstacles usually produce undesirable effects on least squares estimators. Ridge regression estimator is suggested in handling severe multicollinearity while robust estimators such as MM estimator and Least Trimmed Squares (LTS) estimator are recommended in tackling the outlier issues. An even worse scenario is when these two problems occur simultaneously. Combination of both leads to robust ridge regression methods which can be used to handle both conditions simultaneously. In this study, a comparative investigation is carried out to compare the performance between ridge MM and ridge LTS estimators. The Root Mean Square Error (RMSE) and Bias are obtained for each estimator to compare their performances. By using simulation study, Laplace and Cauchy distributions are used in introducing outliers to the simulated data with high multicollinearity ρ = 0.90, 0.95 and 0.98 for sample sizes n=25, 50 and 100. From the results, it is found that Ridge LTS is the best estimator for many combinations of error distributions and degrees of multicollinearity. Similar results were obtained when using two sets of real data.