The efficiency of some robust ridge regression for handling multicollinearity and non-normals errors problems

Abstract

A common problems in multiple regression models are multicollinearity and non-normal errors, which produce undesirable effects on the least squares estimators. So, it would seem important to combine methods of estimation designed to deal with these problems. In this paper, a comparative investigation was done experimentally for some different estimation methods, which namely the ordinary least squares ( LS) , Ridge Regression ( R ), Ridge least Absolute Deviation (RLAD), Weighted Ridge (WR), Robust M(M) and Robust Ridge regression based on M-estimation (RM). From a simulation study, the resulting robust ridge regression estimator (RM)is efficient than other estimators, using the mean squared error criterion for many combinations of error distribution and degree of multicollinearity.