A modified one parameter Liu estimator for Conway-Maxwell Poisson response model

The maximum likelihood estimator (MLE) is generally used to estimate the Conway Maxwell Poisson regression model (COMPRM). When the explanatory variables are highly correlated, then the MLE results are not valid. In this study, we proposed a modified one-parameter Liu estimator in the presence of multicollinearity among the regressors for the COMPRM. The theoretical properties of the proposed estimator are derived and compared it with the available biased estimators as well as the MLE based on the matrix mean squared error (MSE) and scalar MSE criteria. To investigate the efficiency of the proposed estimator, a Monte Carlo simulation analysis was performed under various controlled conditions. Finally, two real applications are considered in the superiority of the proposed estimator. The simulation and real applications results show that the proposed estimator outperforms the classical MLE and other biased estimators in terms of the minimum MSE and mean absolute error criterion .