A comprehensive study on robust Poisson James–Stein estimator for outlier and multicollinearity: Simulation and applications

Poisson regression models (PRMs) are widely used for analyzing count data, but their accuracy can be affected by outliers and multicollinearity, leading to unreliable parameter estimates. Outliers introduce bias and inefficiency in the estimation, while multicollinearity leads to an inflated variance and thus increases the mean squared error and weakens the coefficient reliability. The Poisson maximum likelihood estimator often performs poorly under these conditions. To address these issues, researchers have proposed biased estimators such as the Poisson ridge regression estimator and the Poisson modified ridge-type estimator. However, these methods do not effectively handle both problems at the same time. In this study, we introduce a new estimator, the robust Poisson James–Stein estimator (PMT-JSE), which incorporates transformed M-estimation to improve parameter estimation when outliers and multicollinearity are present. Theoretical conditions for its superiority are established, and a Monte Carlo simulation is conducted to compare its performance with that of existing robust estimators. The results show that PMT-JSE provides more stable and accurate estimates. In addition, two real-world applications confirm its effectiveness. Based on these findings, we recommend PMT-JSE for practitioners working with PRMs affected by outliers and multicollinearity.