Liu-type estimator in Conway–Maxwell–Poisson regression model: theory, simulation and application

Recently, many authors have been motivated to propose a new regression estimator in the case of multicollinearity. The most well-known of these estimators are ridge, Liu and Liu-type estimators. Many studies on regression models have shown that the Liu-type estimator is a good alternative to the ridge and Liu estimators in the literature. We consider a new Liu-type estimator, an alternative to ridge and Liu estimators in Conway–Maxwell–Poisson regression model. Moreover, we study the theoretical properties of the Liu-type estimator, and we provide some theorems showing under which conditions that the Liu-type estimator is superior to the others. Since there are two parameters of the Liu-type estimator, we also propose a method to select the parameters. We designed a simulation study to demonstrate the superiority of the Liu-type estimator compared to the ridge and Liu estimators. We also evaluated the usefulness and superiority of the proposed regression estimator with a practical data example. As a result of the simulation and real-world data example, we conclude that the proposed regression estimator is superior to its competitors according to the mean square error criterion.