Employing Several Methods to Estimate the Generalized Liu Parameter in Multiple Linear Regression Model

Abstract

Multiple linear interferences are a fundamental obstacle in many standard models. This problem appears as a result of linear relationships between two explanatory variables or more. Simulation results show that the generalized Liu regression model was the best and that the contraction parameter proposed was more efficient than the methods presented. As the error variance increases, the value (MSE) increases. When this problem exists in the data, the estimator of the ordinary least squares method will fail because one of the basic assumptions of the method has not been fulfilled. The normal least squares, which state that there is no linear correlation between the explanatory variables, will not get an estimator with the Best Linear Unbiased Estimator (BLUE) feature. The least-squares regression method and the generalized Liu regression method were compared by taking several methods for the generalized Liu parameters and selecting the best contraction parameter for the Liu regression model. The study aims to address the problem of multiple linear interferences by using the general Liu estimator and making a comparison between the methods for estimating the Liu parameter, where several methods were presented, and the best method for estimating the Liu parameter was chosen according to the standard of the sum of error squares as well as a comparison between these methods and the conventional method. Simulation results showed that the generalized Liu coefficient estimate was the best for having the lowest values (MSE) and that the best shrinkage parameter is (G4), the work-based approach.