Quantile-Based Estimation of Liu Parameter in the Linear Regression Model: Applications to Portland Cement and US Crime Data

Abstract

In multiple linear regression models, the multicollinearity problem mostly occurs when the explanatory variables are correlated among each other. It is well known that when the multicollinearity exists, the variance of the ordinary least square estimator is unstable. As a remedy, Liu in [1] developed a new method of estimation with biasing parameter d. In this paper, we have introduced a new method to estimate the biasing parameter in order to mitigate the problem of multicollinearity. The proposed method provides the class of estimators that are based on quantile of the regression coefficients. The performance of the new estimators is compared with the existing estimators through Monte Carlo simulation, where mean squared error and mean absolute error are considered as evaluation criteria of the estimators. Portland cement and US Crime data is used as an application to illustrate the benefit of the new estimators. Based on simulation and numerical study, it is concluded that the new estimators outperform the existing estimators in certain situations including high and severe cases of multicollinearity. 95% mean prediction interval of all the estimators is also computed for the Portland cement data. We recommend the use of new method to practitioners when the problem of high multicollinearity exists among the explanatory variables.