Shrinkage Estimators in Bell Regression Model: Subject Review

Bell regression model has become a very versatile model that replaced the conventional count data models and helps to resolve the problem of over-dispersion where the variance of data points surpasses the mean. Nevertheless, in practice, the classical maximum likelihood estimators (MLE) of the parameters of a model are frequently affected by multicollinearity among the explanatory variables, and they yield highly unstable estimates and inflated variances. To address these difficulties, estimation methods developed to estimate shrinkage, such as ridge or Liu estimators have been applied to the Bell regression model. In the subject review, new developments in estimators of shrinkage of Bell regression models are proportionate in discussing their theoretical background in knowledge, estimation process, and asymptotic characteristics. The results on Monte Carlo simulation studies always show that shrinkage estimators outweigh MLEs in that they minimize mean squared error and bias more than MLEs, especially in cases of multicollinearity. Both overall, estimation methods of shrinkage is a considerable improvement in Bell regression modeling that offers certainty and effectiveness of analysis of complicated counts information utilizing problematic distribution attributes.