Linearized ridge estimator in Poisson-inverse Gaussian regression model

Abstract

This paper suggests a new linearized ridge estimation of the Poisson-Inverse Gaussian Regression Model (PIGRM) which is expected to resolve the problem of multicollinearity and overdispersion in the analyses based on the count data modeling. Using asymptotics of the maximum likelihood estimator (MLE), an advantage of the suggested estimator will be harnessing the possibility of adding a parameter associated with shrinkage in order to stabilize coefficient estimates as well as decrease their variance. Wide-ranging Monte-Carlo analyses were induced to assess selection of the linearized ridge estimator in comparison to conventional MLE and various types of biased estimator in an assortment of circumstances of precinct size, engagingness of predictors and variability. It is showed consistently that linearized ridge estimator exhibits lower values of mean squared error (MSE) which implies its better accuracy in estimation and robustness. In addition, the practical utility of the approach is confirmed by the application to real-world data that demonstrate better model fit and predictive performance. These results indicate that the linearized ridge estimator should be of great use to the reliable inference about PIGRM, particularly with multicollinearity and overdispersion.