Liu-Type Estimator for the Poisson-Inverse Gaussian Regression Model: Simulation and Practical Applications

Abstract

The Poisson-Inverse Gaussian regression model (PIGRM) is commonly used to analyze count datasets with over-dispersion. While the maximum likelihood estimator (MLE) is a standard choice for estimating PIGRM parameters, its performance may be suboptimal in the presence of correlated explanatory variables. To overcome this limitation, we introduce a novel Liu-type estimator for PIGRM. Our analysis includes an examination of the matrix mean square error (MMSE) and scalar mean square error (SMSE) properties of the proposed estimator, comparing them with those of the MLE, ridge, and Liu estimators. We also present several parameters of the Liu-type estimator for PIGRM. We evaluated the performance of the proposed estimator through a simulation study and application to real-life data, using SMSE as the primary evaluation criterion. Our results demonstrate that the proposed estimators outperform the MLE, ridge, and Liu estimators in both simulated and real-world scenarios.