Modelling Colinearity in the Presence of Non–Normal Error: A Robust Regression Approach

Multicollinearity and non-normal errors, which lead to unwanted effect on the least square estimator, are common problems in multiple regression models. It would therefore seem important to combine estimation techniques for addressing these problems. In the presence of multicollinearity and non-normal errors, different estimation techniques were examined, namely, the Ordinary Least Squares (OLS), Ridge Regression (R), Weighted Ridge regression (WR), Robust M-estimation (M), and Robust Ridge Regression with emphasis on M-estimation (RM). When compared with the condition of Collinearity, the results of a simulated study shows that Robust Ridge (RM) provides a more efficient estimate then the other estimators considered. When both Collinearity and non-normal errors were considered, the M-estimators (M) produces a more efficient and precise estimates.

Keywords: Multicollinearity; Ordinary least squares (OLS); Regressor; Simulation; M-estimator; Estimates