Developing a two-parameter Liu estimator for the COM–Poisson regression model: Application and simulation - Abonazel, Mohamed R.; Awwad, Fuad A.; Tag Eldin, Elsayed; Kibria, B. M. Golam; Khattab, Ibrahim G. (Frontiers in Applied Mathematics and Statistics, 2023)
The Conway–Maxwell Poisson (COMP) model is defined as a flexible count regression model used for over– and under–dispersion cases. In regression analysis, when the explanatory variables are highly correlated, this means that there is the multicollinearity problem in the model. This problem increases the standard error of maximum likelihood estimates. To manage the multicollinearity effects in the COMP model, we proposed a new modified Liu estimator based on two shrinkage parameters (k, d). To assess the performance of the proposed estimator, the mean squared error (MSE) criterion is used. Theoretical comparison of the proposed estimator with the ridge, Liu, and modified one–parameter Liu estimators is made. The Monte Carlo simulation and real data application are employed to examine the efficiency of the proposed estimator and compare it with the ridge, Liu, and modified one–parameter Liu estimators. The results showed the superiority of the proposed estimator, as it has the smallest MSE value.