Generalized Kibria-Lukman Estimator: Method, Simulation, and Application - Dawoud, Issam; Abonazel, Mohamed R.; Awwad, Fuad A. (Frontiers in Applied Mathematics and Statistics, 2022)
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 and the recent one is the ridge-type estimator which given by Kibria and Lukman (2020). In this paper, a generalized version of the KL estimator is proposed as well as the optimal biasing parameter of our proposed estimator is 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 are 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 the other estimator, especially, in the case the standard deviation of the errors was large as well as the correlation between the explanatory variables is very high.