Generalized Kibria-Lukman Estimator: Method, Simulation, and Application
İssam Dawoud, Mohamed R. Abonazel, Fuad A. Awwad
Abstract
In the linear regression model, the multicollinearity effects on the ordinary least squares (OLS) estimator performance make it inefficient. To solve this, several estimators are given. The Kibria-Lukman (KL) estimator is a recent estimator that has been proposed to solve the multicollinearity problem. In this paper, a generalized version of the KL estimator is proposed, along with the optimal biasing parameter of our proposed estimator derived by minimizing the scalar mean squared error. Theoretically, the performance of the proposed estimator is compared with the OLS, the generalized ridge, the generalized Liu, and the KL estimators by the matrix mean squared error. Furthermore, a simulation study and the numerical example were performed for comparing the performance of the proposed estimator with the OLS and the KL estimators. The results indicate that the proposed estimator is better than other estimators, especially in cases where the standard deviation of the errors was large and when the correlation between the explanatory variables is very high.