Developing a two-parameter Liu estimator for the COM–Poisson regression model: Application and simulation
The Conway–Maxwell–Poisson (COMP) model is defined as a flexible count regression model used for over- and under-dispersion cases. In regression analysis, when the explanatory variables are highly correlated, this means that there is a multicollinearity problem in the model. This problem increases t...
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Frontiers Media S.A.
2023-02-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2023.956963/full |
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| author | Mohamed R. Abonazel Fuad A. Awwad Elsayed Tag Eldin B. M. Golam Kibria Ibrahim G. Khattab |
| author_facet | Mohamed R. Abonazel Fuad A. Awwad Elsayed Tag Eldin B. M. Golam Kibria Ibrahim G. Khattab |
| author_sort | Mohamed R. Abonazel |
| collection | DOAJ |
| description | The Conway–Maxwell–Poisson (COMP) model is defined as a flexible count regression model used for over- and under-dispersion cases. In regression analysis, when the explanatory variables are highly correlated, this means that there is a multicollinearity problem in the model. This problem increases the standard error of maximum likelihood estimates. To manage the multicollinearity effects in the COMP model, we proposed a new modified Liu estimator based on two shrinkage parameters (k, d). To assess the performance of the proposed estimator, the mean squared error (MSE) criterion is used. The theoretical comparison of the proposed estimator with the ridge, Liu, and modified one-parameter Liu estimators is made. The Monte Carlo simulation and real data application are employed to examine the efficiency of the proposed estimator and to compare it with the ridge, Liu, and modified one-parameter Liu estimators. The results showed the superiority of the proposed estimator as it has the smallest MSE value. |
| first_indexed | 2024-04-10T09:07:21Z |
| format | Article |
| id | doaj.art-17f6c1b4400748c385e1aa9e19de4fe3 |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-04-10T09:07:21Z |
| publishDate | 2023-02-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-17f6c1b4400748c385e1aa9e19de4fe32023-02-21T05:41:51ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872023-02-01910.3389/fams.2023.956963956963Developing a two-parameter Liu estimator for the COM–Poisson regression model: Application and simulationMohamed R. Abonazel0Fuad A. Awwad1Elsayed Tag Eldin2B. M. Golam Kibria3Ibrahim G. Khattab4Department of Applied Statistics and Econometrics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, EgyptDepartment of Quantitative Analysis, College of Business Administration, King Saud University, Riyadh, Saudi ArabiaElectrical Engineering Department, Faculty of Engineering and Technology, Future University in Egypt, New Cairo, EgyptDepartment of Mathematics and Statistics, Florida International University, Miami, FL, United StatesDepartment of Statistics, Mathematics, and Insurance, Faculty of Business, Alexandria University, Alexandria, EgyptThe Conway–Maxwell–Poisson (COMP) model is defined as a flexible count regression model used for over- and under-dispersion cases. In regression analysis, when the explanatory variables are highly correlated, this means that there is a multicollinearity problem in the model. This problem increases the standard error of maximum likelihood estimates. To manage the multicollinearity effects in the COMP model, we proposed a new modified Liu estimator based on two shrinkage parameters (k, d). To assess the performance of the proposed estimator, the mean squared error (MSE) criterion is used. The theoretical comparison of the proposed estimator with the ridge, Liu, and modified one-parameter Liu estimators is made. The Monte Carlo simulation and real data application are employed to examine the efficiency of the proposed estimator and to compare it with the ridge, Liu, and modified one-parameter Liu estimators. The results showed the superiority of the proposed estimator as it has the smallest MSE value.https://www.frontiersin.org/articles/10.3389/fams.2023.956963/fullConway–Maxwell–Poisson modelLiu regression estimatormodified one-parameter Liumulticollinearityridge regression |
| spellingShingle | Mohamed R. Abonazel Fuad A. Awwad Elsayed Tag Eldin B. M. Golam Kibria Ibrahim G. Khattab Developing a two-parameter Liu estimator for the COM–Poisson regression model: Application and simulation Frontiers in Applied Mathematics and Statistics Conway–Maxwell–Poisson model Liu regression estimator modified one-parameter Liu multicollinearity ridge regression |
| title | Developing a two-parameter Liu estimator for the COM–Poisson regression model: Application and simulation |
| title_full | Developing a two-parameter Liu estimator for the COM–Poisson regression model: Application and simulation |
| title_fullStr | Developing a two-parameter Liu estimator for the COM–Poisson regression model: Application and simulation |
| title_full_unstemmed | Developing a two-parameter Liu estimator for the COM–Poisson regression model: Application and simulation |
| title_short | Developing a two-parameter Liu estimator for the COM–Poisson regression model: Application and simulation |
| title_sort | developing a two parameter liu estimator for the com poisson regression model application and simulation |
| topic | Conway–Maxwell–Poisson model Liu regression estimator modified one-parameter Liu multicollinearity ridge regression |
| url | https://www.frontiersin.org/articles/10.3389/fams.2023.956963/full |
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