A new estimator for the multicollinear Poisson regression model: simulation and application.

Area of Science:

• Statistics
• Econometrics
• Data Science

Background:

• The maximum likelihood estimator (MLE) exhibits instability when multicollinearity is present in Poisson regression models (PRM).
• Multicollinearity can significantly affect the reliability of regression coefficient estimates in PRM.

Purpose of the Study:

• To propose a novel biased estimator designed to overcome the instability issue in PRM due to multicollinearity.
• To enhance the estimation of regression coefficients in the presence of multicollinearity.

Main Methods:

• Development of a new estimator incorporating biasing parameters for PRM.
• Conducting simulation experiments to evaluate estimator performance.
• Utilizing the mean squared error (MSE) criterion for performance comparison.

Main Results:

• The proposed estimator demonstrated superior performance compared to existing methods.
• Simulation results indicated the effectiveness of the new estimator in handling multicollinearity.
• Analysis of aircraft damage data confirmed the practical utility of the proposed estimator.

Conclusions:

• The new biased estimator offers a more stable and reliable approach for PRM with multicollinearity.
• The findings suggest practical advantages of the proposed estimator in real-world applications.
• This research contributes a valuable tool for statistical modeling in the presence of multicollinearity.