On the performance of some new ridge parameter estimators in the Poisson-inverse Gaussian ridge regression

Abstract

The Poisson Inverse Gaussian Regression model (PIGRM) is used for modeling the count datasets to deal with the issue of over-dispersion. Generally, the maximum likelihood estimator (MLE) is used to estimate the PIGRM estimates. In the PIGRM, when the explanatory variables are correlated, the MLE does not provide efficient results. To overcome this problem, we propose a ridge estimator for the PIGRM. The matrix mean square error (MSE) and the scalar MSE properties are derived and then compared with the MLE. In the ridge estimator, ridge parameter play a significant role, so, this study also proposes different ridge parameter estimators for the PIGRM. The performance of the proposed estimator is evaluated with the help of a simulation study and a real-life application using MSE as a performance evaluation criterion. The simulation study and the real-life application results show the superiority of the proposed parameter estimators as compared to the MLE.

Keywords

• MLE
• Multicollinearity
• Poisson-inverse Gaussian regression
• Over-dispersion
• Ridge estimator