Classical least squares method for estimating regression models consisting of minimizing the sum of the squared residuals. Some of the assumptions of Ordinary least squares method (OLS) is that there is no correlations (multicollinearity) and extreme values (outliers) between the independent variables. Violation of these assumptions arises most often in regression analysis and can lead to inefficiency of the least square method. This paper therefore determined the efficient estimator between Least Absolute Deviation (LAD) and Weighted Least Square (WLS) in multiple linear regression models at different levels of multicollinearity and outlier in the explanatory variables. Simulation technique were conducted using R Statistical software, to investigate the performance of the two estimators under violation of assumptions of lack of multicollinearity and outliers. Their performances were compared at different sample sizes. Finite properties of estimators' criteria namely, mean absolute error, absolute bias and mean squared error were used for comparing the methods. The best estimator was selected based on minimum value of these criteria at a specified level of multicollinearity, outlier and sample size. The results showed that, LAD was the best at different levels of multicollinearity and outlier and was recommended as alternative to OLS under this condition. The performances of the two estimators decreased when the levels of multicollinearity and outliers was increased.
Warha et al. (Thu,) studied this question.