64th ISI World Statistics Congress - Ottawa, Canada

64th ISI World Statistics Congress - Ottawa, Canada

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


Abdul Majid


  • S
    Shakeel Ahmad
  • M
    Muhammad Aslam


64th ISI World Statistics Congress - Ottawa, Canada

Format: CPS Abstract

Keywords: m-estimator, outlier, regression

Session: CPS 76 - Statistical estimation V

Wednesday 19 July 8:30 a.m. - 9:40 a.m. (Canada/Eastern)


The Liu estimator (LE) is a widely used estimation method to combat the problem of multicollinearity while dealing with the multiple linear regression model. The situation becomes problematic for the LE when the data set is contaminated with outliers in the y-direction. To tackle the issues of multicollinearity and outlier simultaneously, the Liu M-estimator (LME) is proposed in the literature. The estimation of Liu biasing parameter d is very crucial while using the LE and the same phenomenon may happen in the case of LME. This study proposes some robust estimators of d based on robust estimates, for the case of LME. The proposed estimators of Liu parameter increase the efficiency of the LME. To evaluate the performance of proposed estimators, we use the Monte Carlo simulations and a real application where the mean squared error is considered as a performance evaluation criterion. Results show a better performance of the LME with our proposed estimators of d as compared to the ordinary least squares estimator, M-estimator, the LE and the existing robust estimators of d.