Alternative ridge robust regression estimator for dealing with collinear influential data points

Abstract

The multicollinearity in multiple linear regression models and the existence of influential data points are common problems. These problems exert undesirable effects on the least squares estimators. So, it is very important to introduce some alternative biased estimators of the robust ridge regression to overcome the influence of these problems simultaneously. In this paper, alternative biased robust regression estimator is defined by mixing the ridge estimation technique into the robust least median squares estimation to obtain the Ridge Least Median Squares (RLMS). The efficiency of the combined estimator (RLMS) is compared with some existing regression estimators, which namely, the Ordinary Least Squares (LS); Ridge Regression (RR) and Ridge Least Absolute Deviation (RLAD). The numerical results of this study show that, the RLMS regression estimator is more efficient than other estimators, based on, Bias and mean squared error criteria for many combinations of influential data points and degree of multicollinearity.

A Comparison of Different Ridge Parameters under Both Multicollinearity and Heteroscedasticity

“…Mansson and Shukur [19] have investigated some logistic ridge regression parameters and they have shown that there is at least one ridge regression estimator that has a lower mean square error than the maximum likelihood method for all situations. Salam [20] has introduced an alternative procedure having a smaller mean square error for determining the ridge parameter. Khalaf [21] proposes two ridge regression parameters and demonstrates the performance of the proposed estimators outperforming the OLS and other estimators.…”