Some Modified Kibria-Lukman Estimators for the Gamma Regression Model

Abstract

This paper aims to propose the Gamma modified Kibria-Lukman estimator according to some selected formulas of the shrinkage parameter in order to overcome the effect of the multicollinearity problem in the Gamma regression model.The properties of the proposed estimator and the conditions of its superiority against the maximum likelihood estimator, Gamma ridge estimator, and Gamma Kibria-Lukman estimator based on the matrix of mean squared error criterion are presented.In addition, some selected formulas for the shrinkage parameter are used to improve the results of estimation.Moreover, a Monte Carlo simulation experiment and an application are implemented to assess the performance of the proposed estimator according to some selected formulas of the shrinkage parameter compared with other existing estimators by the scalar mean squared error criterion.The results confirm that the proposed estimator, the Gamma modified Kibria-Lukman estimator is preferred over other existing estimators in terms of scalar mean squared error.