Performance of alternative estimators in the Poisson-Inverse Gaussian Regression model: simulation and application

The Poisson-Inverse Gaussian Regression model (PIGRM) is applied for the modeling of count datasets with over-dispersion. The PIGRM estimates are estimated using the maximum likelihood estimator (MLE). When the explanatory variables in the PIGRM are correlated, the MLE does not produce useful findings. In this work, some biased estimators, i.e. Stein, ridge, Liu and modified Liu estimators, are adapted to resolve the issue of multicollinearity in the PIGRM. These biased estimators have different behaviors for different models, which is why these are considered for the PIGRM to identify the best one. Every biased estimator has a biasing parameter with some limitations. The Liu parameter (d) in the Liu estimator mostly does not lie between 0 and 1. To overcome this limitation, the improvement of the Liu estimator in the PIGRM is considered an alternative to the Liu estimator. Additionally, some bias parameters were used for the Stein estimator. The performance of estimators is evaluated with the help of a simulation study and a real-life application based on the minimum mean squared error criterion. The simulation and application findings favor the ridge estimator with specific biasing parameters because it provides less variation than others.