A New Kibria-Lukman-Type Estimator for Poisson Regression Models

Year 2024, , 199 - 212, 31.12.2024

Cemal Çiçek , Kadri Ulaş Akay

https://doi.org/10.26650/acin.1558583

Abstract

One of the most important models for the analysis of count data is the Poisson Regression Model (PRM). The parameter estimates of the PRM are obtained by the Maximum Likelihood Estimator (MLE). However, MLE is adversely affected in the presence of multicollinearity, which is known as the approximately linear relationship between the explanatory variables. Many shrinkage estimators have been proposed to reduce the effects of multicollinearity in PRMs. As an alternative to other biased estimators that are already in use in PRMs, we presented a novel estimator in this paper that is based on the Kibria-Lukman estimator. The superiority of the proposed new biased estimator over existing biased estimators is given by the asymptotic matrix mean square error. Furthermore, two separate Monte Carlo simulation studies are conducted to investigate the performance of the proposed biased estimators. Finally, real data is used to examine the superiority of the proposed estimator.

Keywords

Mean squared error, multicollinearity, poisson liu estimator, poisson regression, poisson ridge estimator

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