Modified jackknife Kibria-Lukman estimator for the Poisson regression model

Poisson regression is one of the methods to analyze count data and, the regression parameters are usually estimated using the maximum likelihood (ML) method. However, the ML method is sensitive to multicollinearity. Multicollinearity occurs when there is linear dependency among the explanatory variables. Multicollinearity often leads to unstable maximum likelihood estimates. In this article, we developed modified jackknifed Poisson Kibria-Lukman (MJPKL) estimator to mitigate multicollinearity in the Poisson regression model. We theoretically compared the MJPKL estimator with some existing estimators and obtained the condition for the superiority of MJPKL. A simulation study and real-life application were conducted to compare the performance of the estimators. It is evident from the simulation and real-life results that the modified jackknifed Poisson K-L estimator (MJPKLE) gives better results than other estimators under some conditions. Finally, the MJPKL estimator reduces the bias of the PKL estimator and dominates every estimator considered in this article.