Weighted ridge M-estimator in the presence of multicollinearity

Abstract

This study is about a development of weighted ridge M-estimator (WRM) which is believed to be a potential estimator in remedying the problems of multicollinearity under both assumptions of normality and non-normality error distributions. The proposed method has been compared with several existing estimators, namely ordinary least squares (OLS), ridge regression (RIDGE), weighted ridge (WRID) and ridge MM-estimator (RMM) using two criteria; bias and root mean square error (RMSE). In addition, the efficiency of the proposed method to the alternatives has been examined using simulation. In general, it has been found that the proposed estimator scores efficiently against the four existing estimators, particularly in the presence of high multicollinearity and under the non-normality error distribution.