On Some Robust Liu Estimators for the Linear Regression Model with Outliers: Theory, Simulation and Application

The Liu estimator (LE) is a widely used estimation method for multiple linear regression model to combat the problem of multicollinearity. The LE is sensitive to the presence of outliers in y-direction. To tackle the simultaneous issue of multicollinearity and outlier in the multiple linear regression model, the Liu M-estimator (LME) is proposed in the literature. The selection of proper estimator for Liu parameter d is very crucial when using the LE as well as for the case of LME. However, this issue has not gained much attention of the researchers in the case of LME. This study proposes some robust estimators of d based on robust estimates for the case of LME. The performance of proposed estimators is compared with the available estimators of d using the Monte Carlo simulations and a real application where the mean squared error is considered as a performance evaluation criterion. Results show a superb performance of the proposed robust estimators as compared to the LE, ordinary least squares and M-estimation methods.