A bias-reduced estimator for generalized Poisson regression with application to carbon dioxide emission in Canada.

The generalized Poisson regression model (GPRM) provides a flexible framework for modeling count data, especially those exhibiting over- or underdispersion. Although the generalized Poisson maximum likelihood estimator is considered the standard method for estimating the parameters of this model, its reliability and accuracy are severely affected by the presence of multicollinearity among explanatory variables. Multicollinearity inflates the variance of parameter estimates, undermining the validity of statistical inference and ultimately leading to unstable and unreliable estimators. To mitigate these problems, this study presents the ridge estimator as a robust alternative within the GPRM framework. Several new strategies are proposed for selecting the optimal value of the ridge parameter. The statistical properties of the proposed ridge estimator were theoretically studied. Theoretical comparisons and extensive Monte Carlo simulations demonstrated a clear and significant superiority of the ridge estimator under multicollinearity conditions, confirming its robustness and efficiency. To demonstrate the scientific and practical relevance of the proposed estimator, it was applied to a real-world case study modeling carbon dioxide emissions in Canada. The results of this experimental application conclusively confirmed the simulation and theoretical comparison results, with the ridge estimator providing more stable and interpretable results than the conventional method, making it a valuable tool for researchers and decision makers in analyzing multicollinear environmental and economic data.