International Journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN: 2313-626X

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 Volume 11, Issue 7 (July 2024), Pages: 49-56

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 Original Research Paper

Stein estimation in the Conway-Maxwell Poisson model with correlated regressors

 Author(s): 

 Faiza Sami 1, Muhammad Amin 1, *, Sadiah M. A. Aljeddani 2

 Affiliation(s):

 1Department of Statistics, University of Sargodha, Sargodha, Pakistan
 2Department of Mathematics, Al-Lith College, Umm Al-Qura University, Al-Lith, Saudi Arabia

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0002-7431-5756

 Digital Object Identifier (DOI)

 https://doi.org/10.21833/ijaas.2024.07.006

 Abstract

The Poisson regression model (PRM) is widely used for count data, applicable when the response variable follows a Poisson distribution with equal dispersion. The Conway-Maxwell Poisson regression model (COMPRM) is more flexible and can handle both under-dispersion and over-dispersion. However, the COMPRM may involve correlated regressors, leading to multicollinearity, which makes the maximum likelihood estimator (MLE) inefficient. Biased estimation methods can address multicollinearity in data. This study proposes a Stein estimator, a biased estimation method, for the COMPRM that can simultaneously address correlated regressors and dispersion issues. The estimated mean square error (EMSE) is used to evaluate performance. The proposed estimator's performance is assessed both theoretically and numerically. The numerical evaluations include a simulation study under various parametric conditions and a real-world application. The results from both the simulation study and the real application demonstrate that the Stein estimator outperforms the MLE.

 © 2024 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords

 Conway-Maxwell Poisson regression, Correlated regressors, Stein estimator, Mean squared error, Multicollinearity

 Article history

 Received 25 January 2024, Received in revised form 18 June 2024, Accepted 26 June 2024

 Acknowledgment 

No Acknowledgment.

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

 Sami F, Amin M, and Aljeddani SMA (2024). Stein estimation in the Conway-Maxwell Poisson model with correlated regressors. International Journal of Advanced and Applied Sciences, 11(7): 49-56

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 Tables

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