A new adjusted Liu estimator for the Poisson regression model

The Poisson regression model (PRM) is usually applied in the situations when the dependent variable is in the form of count data. For estimating the unknown parameters of the PRM, maximum likelihood estimator (MLE) is commonly used. However, its performance is suspected when the regressors are multicollinear. The performance of MLE is not satisfactory in the presence of multicollinearity. To mitigate this problem, different biased estimators are discussed in the literature, that is, ridge and Liu. However, the drawback of using the traditional Liu estimator is that in most of the times, the shrinkage parameter d, attains a negative value which is the major disadvantage of traditional Liu estimator. So, to overcome this problem, we propose a new adjusted Poisson Liu estimator (APLE) for the PRM which is the robust solution to the problem of multicollinear explanatory variables. For assessment purpose, we perform a theoretical comparison with other competitive estimators. In addition, a Monte Carlo simulation study is conducted to show the superiority of the new estimator. At the end, two real life applications are also considered. From the findings of simulation study and two empirical applications, it is observed that the APLE is the most robust and consistent estimation method as compared to the MLE and other competitive estimators.