Improving generalized ridge estimator for the gamma regression model.

Abstract

It has been consistently proven that the ridge estimator is an effective shrinking strategy for reducing the effects of multicollinearity. An effective model to use when the response variable is positively skewed is the Gamma Regression Model (GRM).  However, it is well known that the existence of multicollinearity can have a detrimental impact on the variance of the maximum likelihood estimator (MLE) of the gamma regression coefficients. The generalized ridge estimator is suggested in this study as a solution to the ridge estimator's limitation. The shrinkage matrix has been estimated using a number of different techniques. Our Monte Carlo simulation and actual data application findings indicate that the suggested estimator, regardless of the kind of estimating method of shrinkage matrix, is superior to the MLE and ridge estimator in terms of Mean Square Error (MSE). Additionally, compared to other methods, some shrinkage matrix estimation techniques can significantly enhance results.