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A new almost unbiased general ridge-type estimator for fitting Poisson regression model with multicollinearity.

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Titel: A new almost unbiased general ridge-type estimator for fitting Poisson regression model with multicollinearity.
Autoren: Alghamdi, Fatimah M.1 (AUTHOR), Hammad, Ali T.2 (AUTHOR), Abd-Elmougod, Gamal A.3 (AUTHOR), Abd El-Raouf, M. M.4 (AUTHOR), Gemeay, Ahmed M.2 (AUTHOR) ahmed.gemeay@science.tanta.edu.eg
Quelle: Statistics. Nov2025, p1-35. 35p. 9 Illustrations.
Schlagwörter: *POISSON regression, *MULTICOLLINEARITY, *PARAMETER estimation, *MAXIMUM likelihood statistics, *SIMULATION methods & models
Abstract: The Poisson regression model (PRM) is widely used for modeling count data. The maximum likelihood estimator (MLE) is used to estimate the parameters of a PRM. However, the MLE is inefficient in the presence of multicollinearity, which leads to inaccurate estimation, reliability, and variance inflation, thus increasing the scalar mean squared error (SMSE). To address this problem, several biased estimators have been proposed. When the biasing parameter is large, biased estimators can exhibit significant bias, so the almost-unbiased estimators are proposed as an alternative. Therefore, this paper presents an almost unbiased general ridge-type estimator to handle the multicollinearity problem in PRM effectively. The performance of the proposed estimator is evaluated through theoretical comparisons with existing estimators and a Monte Carlo simulation study, which demonstrates the superiority of the proposed estimator over existing estimators. Finally, the performance of the proposed estimator is demonstrated using real data, providing researchers with more reliable and less biased solutions than analyzing multicollinear data in a PRM. [ABSTRACT FROM AUTHOR]
Datenbank: Academic Search Index
Beschreibung
Abstract:The Poisson regression model (PRM) is widely used for modeling count data. The maximum likelihood estimator (MLE) is used to estimate the parameters of a PRM. However, the MLE is inefficient in the presence of multicollinearity, which leads to inaccurate estimation, reliability, and variance inflation, thus increasing the scalar mean squared error (SMSE). To address this problem, several biased estimators have been proposed. When the biasing parameter is large, biased estimators can exhibit significant bias, so the almost-unbiased estimators are proposed as an alternative. Therefore, this paper presents an almost unbiased general ridge-type estimator to handle the multicollinearity problem in PRM effectively. The performance of the proposed estimator is evaluated through theoretical comparisons with existing estimators and a Monte Carlo simulation study, which demonstrates the superiority of the proposed estimator over existing estimators. Finally, the performance of the proposed estimator is demonstrated using real data, providing researchers with more reliable and less biased solutions than analyzing multicollinear data in a PRM. [ABSTRACT FROM AUTHOR]
ISSN:02331888
DOI:10.1080/02331888.2025.2581835