The comparison between several robust ridge regression estimators in the presence of multicollinearity and multiple outliers

Abstract

In the presence of multicollinearity and multiple outliers, statistical inference of linear regression model using ordinary least squares (OLS) estimators would be severely affected and produces misleading results. To overcome this, many approaches have been investigated. These include robust methods which were reported to be less sensitive to the presence of outliers. In addition, ridge regression technique was employed to tackle multicollinearity problem. In order to mitigate both problems, a combination of ridge regression and robust methods was discussed in this study. The superiority of this approach was examined when simultaneous presence of multicollinearity and multiple outliers occurred in multiple linear regression. This study aimed to look at the performance of several well-known robust estimators; M, MM, RIDGE and robust ridge regression estimators, namely Weighted Ridge M-estimator (WRM), Weighted Ridge MM (WRMM), Ridge MM (RMM), in such a situation. Results of the study showed that in the presence of simultaneous multicollinearity and multiple outliers (in both x and y-direction), the RMM and RIDGE are more or less similar in terms of superiority over the other estimators, regardless of the number of observation, level of collinearity and percentage of outliers used. However, when outliers occurred in only single direction (y-direction), the WRMM estimator is the most superior among the robust ridge regression estimators, by producing the least variance. In conclusion, the robust ridge regression is the best alternative as compared to robust and conventional least squares estimators when dealing with simultaneous presence of multicollinearity and outliers.