A New Two-Parameter Estimator for the Poisson Regression Model

It is known that multicollinearity affects the maximum likelihood estimator (MLE) negatively when estimating the coefficients in Poisson regression. Namely, the variance of MLE inflates and the estimations become instable. Therefore, in this article we propose a new two-parameter estimator (TPE) and some methods to estimate these two parameters for the Poisson regression model when there is multicollinearity problem. Moreover, we conduct a Monte Carlo simulation to evaluate the performance of the estimators using mean squared error (MSE) criterion. We finally consider a real data application. The simulations results show that TPE outperforms MLE in almost all the situations considered in the simulation and it has a smaller MSE and smaller standard errors than MLE in the application.