A NEW CLASS OF ROBUST POISSON RIDGE-TYPE ESTIMATOR: SIMULATION AND THEORY APPROACH

Abstract

This study evaluates the performance of various Poisson regression estimators under conditions of multicollinearity and data contamination (outliers) using simulated data. Specifically, the mean squared errors (MSEs) of traditional estimators Robust Poisson Maximum Likelihood Estimator (RPMLE), Robust Poisson Ridge (RPR), Robust Poisson Liu (RPL), and Robust Poisson Kibria–Lukman (RPK-L) were compared with three newly proposed estimators (prop1, prop1ME, and prop1HM) across different sample sizes (n = 200, 300, 400), correlation strengths (ρ = 0.8–0.99), and contamination levels (τ = 20%). Results consistently show that RPMLE yields the highest MSE, confirming its vulnerability to outliers and multicollinearity. While classical shrinkage methods perform better than RPMLE, their efficiency declines with increasing ρ and τ. In contrast, the proposed estimators demonstrate superior robustness, with prop1HM achieving the lowest MSE across nearly all designs. Notably, prop1HM maintains its performance even under high multicollinearity and small sample sizes, highlighting its adaptability. As contamination intensifies, the performance gap between the proposed and traditional estimators widens, emphasizing the resilience of the new methods. These findings suggest that prop1HM, in particular, is a reliable and efficient alternative for Poisson regression analysis in the presence of multicollinearity and outlier contamination.