Robust biased estimators for Poisson regression model: Simulation and applications

• Published in: Concurrency and computation Vol. 35; no. 7
• Main Authors: Lukman, Adewale F., Arashi, Mohammad, Prokaj, Vilmos
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 25-03-2023; Wiley Subscription Services, Inc
• Subjects: conditionally unbiased bounded influence estimator; Estimators; multicollinearity; outlier; Poisson density functions; Regression models; ridge estimator; robust CE; robust MT; Robustness (mathematics); Statistical models; transformed M‐estimator
• ISSN: 1532-0626; 1532-0634
• DOI: 10.1002/cpe.7594

Summary
The method of maximum likelihood flops when there is linear dependency (multicollinearity) and outlier in the generalized linear models. In this study, we combined the ridge estimator with the transformed M‐estimator (MT) and the conditionally unbiased bounded influence estimator (CE). The two new estimators are called the robust MT estimator and Robust‐CE. A Monte Carlo study revealed that the proposed estimators dominate for the generalized linear models with Poisson response and log link function. The real‐life application results support the simulation outcome.