A New Biased Estimation Class to Combat the Multicollinearity in Regression Models: Modified Two--Parameter Liu Estimator

The multicollinearity problem occurrence of the explanatory variables affects the least-squares (LS) estimator seriously in the regression models. The multicollinearity adverse effects on the LS estimation are also investigated by many authors. Instead of the LS estimator, we propose a new modified two–parameter Liu (MTPL) estimator to handle the multicollinearity for the regression model based on two shrinkage parameters (k, d). Also, we give the necessary andsufficient conditions for the outperforming of the proposed MTPL estimator over the LS, ridge, Liu, Kibria-Lukman (KL), modified ridge type (MRT), and modified one–parameter Liu (MOPL) estimators by the scalar mean squared error (MSE) criterion. Optimal biasing parameters of the proposed MTPL estimator are derived. Simulation and real data are used to study the efficiency of the MTPL estimator. The results of the simulation study and two real-life applications show thesuperiority of the proposed estimator because the MSE of the proposed estimator is smaller than the other estimators.