Modified Kibria–Lukman Estimator for the Conway–Maxwell–Poisson Regression Model: Simulation and Application

Nasser A. Alreshidi, Masad A. Alrasheedi, Adewale F. Lukman (), Hleil Alrweili and Rasha A. Farghali
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Nasser A. Alreshidi: Department of Mathematics, College of Science, Northern Border University, Arar 73213, Saudi Arabia
Masad A. Alrasheedi: Department of Management Information Systems, College of Business Administration, Taibah University, Al-Madinah Al-Munawara 42353, Saudi Arabia
Adewale F. Lukman: Department of Mathematics and Statistics, University of North Dakota, Grand Forks, ND 58202, USA
Hleil Alrweili: Department of Mathematics, College of Science, Northern Border University, Arar 73213, Saudi Arabia
Rasha A. Farghali: Department of Mathematics, Insurance and Applied Statistics, Helwan University, Cairo 11795, Egypt

Mathematics, 2025, vol. 13, issue 5, 1-20

Abstract: This study presents a novel estimator that combines the Kibria–Lukman and ridge estimators to address the challenges of multicollinearity in Conway–Maxwell–Poisson (COMP) regression models. The Conventional COMP Maximum Likelihood Estimator (CMLE) is notably susceptible to the adverse effects of multicollinearity, underscoring the necessity for alternative estimation strategies. We comprehensively compare the proposed COMP Modified Kibria–Lukman estimator (CMKLE) against existing methodologies to mitigate multicollinearity effects. Through rigorous Monte Carlo simulations and real-world applications, our results demonstrate that the CMKLE exhibits superior resilience to multicollinearity while consistently achieving lower mean squared error (MSE) values. Additionally, our findings underscore the critical role of larger sample sizes in enhancing estimator performance, particularly in the presence of high multicollinearity and over-dispersion. Importantly, the CMKLE outperforms traditional estimators, including the CMLE, in predictive accuracy, reinforcing the imperative for judicious selection of estimation techniques in statistical modeling.

Keywords: COMP regression models; multicollinearity; over-dispersion; Kibria–Lukman estimator; ridge estimator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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