Performance of some ridge estimators for the gamma regression model

In this study, we proposed some ridge estimators by considering the work of Mansson (Econ Model 29(2):178-184, 2012), Dorugade (J Assoc Arab Univ Basic Appl Sci 15:94-99, 2014) and some others for the gamma regression model (GRM). The GRM is a special form of the generalized linear model (GLM), where the response variable is positively skewed and well fitted to the gamma distribution. The commonly used method for estimation of the GRM coefficients is the maximum likelihood (ML) estimation method. The ML estimation method perform better, if the explanatory variables are uncorrelated. There are the situations, where the explanatory variables are correlated, then the ML estimation method is incapable to estimate the GRM coefficients. In this situation, some biased estimation methods are proposed and the most popular one is the ridge estimation method. The ridge estimators for the GRM are proposed and compared on the basis of mean squared error (MSE). Moreover, the outperforms of proposed ridge estimators are also calculated. The comparison has done using a Monte Carlo simulation study and two real data sets. Results show that Kibria's and Mansson and Shukur's methods are preferred over the ML method.