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Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation
Benedicta B Aladeitan1,2, Olukayode Adebimpe1,2, Adewale F Lukman1,2
1Department of Physical Sciences, (Mathematics) Landmark University, Omu-Aran, Kwara State, +234, Nigeria.
F1000Research
|February 21, 2022
Summary
This study introduces a modified Kibria-Lukman (KL) estimator to improve the Poisson Regression Model in the presence of multicollinearity. The new estimator demonstrates superior efficiency compared to existing methods, including the Maximum Likelihood Estimator (MLE).
Area of Science:
- Statistics
- Econometrics
Background:
- Multicollinearity negatively impacts Maximum Likelihood Estimator (MLE) efficiency in linear and generalized linear models.
- Existing alternatives like ridge, Liu, and Kibria-Lukman (KL) estimators have limitations.
- The KL estimator is often preferred but requires modification for specific models.
Purpose of the Study:
- To modify the Kibria-Lukman (KL) estimator for enhanced performance in Poisson Regression Models.
- To address the challenges posed by multicollinearity in statistical modeling.
- To develop a more efficient estimator for Poisson regression under multicollinearity.
Main Methods:
- A simulation study was conducted to evaluate estimator performance.
- A real-life case study was used for practical validation.
- The proposed modified KL estimator was compared against established estimators.
Main Results:
- The modified KL estimator significantly outperformed the MLE, Poisson Ridge Regression Estimator (PRE), Poisson Liu Estimator (PLE), and the standard Poisson KL (PKL) estimator in simulations.
- Simulation results indicated improved efficiency and stability.
- The real-life application corroborated the findings from the simulation study.
Conclusions:
- The modified KL estimator is a more efficient alternative for Poisson Regression Models when multicollinearity is present.
- This new estimator effectively mitigates the adverse effects of multicollinearity.
- The study recommends the use of the modified KL estimator for improved statistical analysis in such scenarios.
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