On the generalized biased estimators for the gamma regression model: methods and applications

Abstract

The gamma regression model (GRM) is commonly used if the response variable is continuous and positively skewed. In the existence of multicollinearity problem, maximum likelihood estimator (MLE) is inadequate for estimating the GRM coefficients. To avoid this issue, well-known estimators such as, ridge and Liu are generally used. In this study, we propose the generalized class of biased estimators, namely generalized ridge, and generalized Liu estimators for the GRM with correlated explanatory variables. The standard properties of the proposed estimators are derived and illustrated using Monte Carlo simulation study and two real applications where mean squared error is considered as an assessment criterion. Based on the findings of simulation and empirical applications, we found that the performance of the generalized gamma ridge regression estimator is better as compared to MLE, and generalized gamma Liu estimator.

Keywords:

• Gamma regression model
• Generalized ridge estimator
• Generalized Liu estimator
• Maximum likelihood estimator
• Multicollinearity