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Adaptive estimation methods for poisson regression: Two-parameter transformed M-estimator
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DOI：10.1016/j.aej.2025.11.032.png)
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Abstract
En 中文
Poisson regression is a widely used framework for modeling count data, with parameters commonly estimated by maximum likelihood. However, the maximum likelihood estimator can suffer from inflated variance in the presence of multicollinearity, leading to a loss of efficiency, and can be distorted by outliers, reducing interpretability of the estimated effects. When both problems occur together, the reliability of inference is further compromised. This paper introduces a new robust estimator designed to address these challenges within the Poisson regression setting. We establish its theoretical properties and clarify its connections to existing shrinkage and robust estimation methods. Simulation studies, evaluated under mean squared error criteria, demonstrate improved efficiency and interpretability relative to competing approaches. Finally, two real data applications highlight the practical advantages of the proposed method.
Keywords:
Poisson regression
Estimator
Monte Carlo simulation
Multicollinearity
Outlier
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