Kibria-Lukman Hybrid Estimator for the Conway–Maxwell–Poisson Regression Model

The Conway-Maxwell-Poisson regression (CMPR) model provides a flexible framework for analyzing count data in cases of overand under-dispersion. Estimating the parameter in CMPR typically relies on the maximum likelihood estimator (MLE), which can be challenging, mainly when multicollinearity exists. In such cases, many estimators offer alternatives to MLE, but often with a more considerable bias. This paper introduces a new hybrid estimator, combining the modified ridge-type estimator's robustness with the KibriaLukman estimator's efficiency, named the Kibria-Lukman hybrid estimator (KLHE). We propose that KLHE address multicollinearity in CMPR, demonstrating its performance through Monte Carlo simulations. The effectiveness of KLHE is highlighted by its ability to handle multicollinearity, resulting in improved estimation accuracy compared to other estimators. We illustrate the practical application of KLHE using a real dataset, demonstrating its potential to enhance parameter estimation in CMPR models, particularly in settings with prevalent multicollinearity. KLHE is a valuable addition to the statistical toolkit, providing researchers with a robust and efficient means to address multicollinearity in CMPR modeling.