Alternative biased estimator based on least trimmed squares for handling collinear leverage data points

Abstract

The multicollinearity in multiple linear regression models and the existence of leverage data points are common problems. These problems exert undesirable effects on the least squares estimators. So, it would seem important to combine methods of estimation designed to deal with these problems simultaneously. In this paper, alternative biased robust regression estimator is defined by mixing the ridge estimation technique into the robust least trimmed squares estimation to obtain the Ridge Least Trimmed Squares (RLTS). The efficiency of the combined estimator(RLTS) 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 RLTS regression estimator is more efficient than other estimators, based on, Bias and mean squared error criteria for many combinations of leverage data points and degree of multicollinearity.