A new class of Poisson Ridge-type estimator

Area of Science:

• Statistics
• Econometrics
• Biostatistics

Background:

• Poisson Regression Models (PRMs) are standard for count data analysis.
• Maximum Likelihood Estimator (MLE) in PRMs is sensitive to multicollinearity.
• Existing biased estimators like PRE, PLE, PLTE, and ILTE aim to mitigate multicollinearity.

Purpose of the Study:

• To propose a new general class of biased estimators for PRMs.
• To address the limitations of MLE in the presence of multicollinearity.
• To offer a superior alternative to existing biased estimators.

Main Methods:

• Development of a novel biased estimator class based on the Poisson Ridge Estimator (PRE).
• Theoretical analysis of the proposed estimator's superiority using asymptotic matrix mean square error.
• Empirical evaluation through two Monte Carlo simulation studies.
• Validation using real-world count data.

Main Results:

• The proposed biased estimator demonstrates superior performance compared to existing estimators.
• Simulation studies confirm the enhanced stability and accuracy of the new estimator.
• Real data analysis validates the practical applicability and effectiveness of the proposed method.

Conclusions:

• The newly proposed biased estimator class offers a robust solution for PRMs with multicollinearity.
• This research contributes a valuable tool for count data analysis in various scientific fields.
• The findings suggest improved parameter estimation and model reliability in the presence of multicollinearity.