Liu-Type Negative Binomial Regression: A Comparison of Recent Estimators and Applications

This chapter introduces a new biased estimator, that is a generalization of Liu-type estimator (Liu in Commun Stat Theory Methods 32:1009–1020 2003), for the negative binomial regression model. Since the variance of the maximum likelihood estimator (MLE) is inflated when there is multicollinearity between the explanatory variables, a new biased estimator is proposed to solve the problem and decrease the variance of MLE in order to make stable inferences. Moreover, we obtain some theoretical comparisons between the new estimator and some other existing estimators via matrix mean squared error criterion. Furthermore, a Monte Carlo simulation study is designed to evaluate performance of the estimators in the sense of mean squared error. Finally, real data applications are used to illustrate the benefits of new estimator.