A new estimator of the gamma regression model: theory, simulation, and application to body fat data

Abstract

The gamma regression model, a specialized generalized linear model, effectively analyzes continuous, positive, and potentially skewed dependent variables when standard linear regression assumptions are violated. However, this model remains susceptible to the multicollinearity problem. Therefore, in this paper we propose a novel two-parameter shrinkage estimator (GDK) to address this problem, theoretically establishing its relationship with existing estimators through formal theorems. Through comprehensive Monte Carlo simulations examining various collinearity scenarios and a real-world numerical application, we demonstrate the GDK estimator's superior performance via mean squared error comparisons. Both simulation results and empirical evidence confirm that our proposed estimator outperforms existing alternatives, offering improved reliability for gamma regression analyses when multicollinearity is present.