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. Keywards: Influential Data Points; Multicollinearity; Ridge regression; Ridge Least Absolute Deviation; Ridge Least Median Squares estimation; Bias and Mean Squared Error criteria