Performance of the Generalized shrinkage Estimator in Zero-Inflated Bell Regression Model

Abstract

The Poisson regression model is an important analytic tool that should be used in count data modeling. When the value of excess dispersion of variables, then the model is not appropriate to apply in case the value of the mean is not equal to the value of the variance of the Poisson distribution. The results are compatible with data when there is the use of Bell regression model. The number of zeros in the count data that is seen is very high. In this case, the Zero-Inflated Bell regression model is an alternative to the Bell regression model. Parameters of the Zero-Inflated Bell regression model are estimated mostly through the approach of maximum likelihood. In an extended linear model, in which the response variable is modeled by two or more explanatory variables, as in the Zero-Inflated Bell regression model, linear dependence is a threat in a real-life analysis. It reduced the maximum likelihood estimator in its effectiveness. In a bid to solve this issue, this paper explores the performance of the generalized shrinkage estimator in the zero-inflated Bell regression model. The superiority of the proposed approaches over the traditional maximum likelihood estimator is validated by results of the simulations and implementations.