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

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 estima-tor (MLE) is used to estimate the PIGRM estimates. In the PIGRM, when the explanatory vari-ables 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 param-eter 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. (c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Automated summary

The Poisson Inverse Gaussian Regression model (PIGRM) is proposed to model count datasets and address over-dispersion. The maximum likelihood estimator (MLE) is commonly used for PIGRM, but it is not efficient when the explanatory variables are correlated. To overcome this issue, a ridge estimator is proposed and its properties are compared with MLE. Different ridge parameter estimators are also proposed. Simulation and real-life application results demonstrate the superiority of the proposed estimators over MLE using MSE as the performance evaluation criterion.