Generalized Ridge Estimator for Conway-Maxwell Poisson Regression Model
DOI:
https://doi.org/10.62933/1nzxxd87Keywords:
Ridge Estimator , Regression Model , Conway-Maxwell Poisson , MulticollinearityAbstract
The ridge estimator has been shown time and again as a preferable shrinkage strategy to counter the impacts of multicollinearity. Interestingly, the Conway-Maxwell Poisson regression model is one of the most frequently used models in application in cases where the response variable is positively skewed. However, its is a well established fact that the variance of maximum likelihood estimator (MLE) of the Conway-Maxwell Poisson regression coefficients can get dragged down due to multicollinearity. Thus, in this paper, a new approach named the generalized ridge estimator is developed to fix the flaw of the ridge estimator. Many methods for estimating the shrinkage matrix have been borrowed. These findings, based on our Monte Carlo simulation and the using of real data application results encourage us: No matter no what kind of estimating method of shrinkage matrix, the proposed estimator is better than MLE estimator and ridge estimator, in terms of MSE. In addition, some estimating method of shrinkage matrix can make the improvement relatively large as compared with others.
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