A new Liu-type estimator for the gamma regression model

Abstract

In many real-world problems, there are situations where the dependent variable may have a Gamma distribution. The Gamma Regression Models (GRMs) are preferred when the response variable assumes a Gamma distribution with a given set of independent variables. The Maximum Likelihood Estimator (MLE) is used to estimate the unknown parameters. In the presence of multicollinearity, the variance of the MLE becomes inflated and the inference based on the MLE may not be reasonable. In this article, we propose a new biased estimator called the new Liu-type estimator in the GRMs to combat multicollinearity. The proposed estimator is a general estimator which includes other biased estimators, such as the Gamma ridge estimator, Gamma Liu estimator, and the estimators with two biasing parameters as special cases. Furthermore, several methods are proposed to determine the biasing parameters in the estimators. Also, a Monte Carlo simulation study has been conducted to assess the performance of the proposed biased estimator where the Estimated Mean Squared Error (EMSE) is considered as a performance criterion. Finally, two numerical examples are given to investigate the performance of the proposed estimator over existing estimators.