Liu-type shrinkage strategies in zero-inflated negative binomial models with application to Expenditure and Default Data

In modeling count data with overdispersion and extra zeros, zero-inflated negative binomial (ZINB) regression model is useful. In a regression model, the multicollinearity problem arises when there are some high correlations between predictor variables. This problem leads to the maximum likelihood method will not be an efficient estimator. The ridge and Liu-type estimators have been proposed to combat the multicollinearity problem so that the Liu-type estimator is better. In this paper, we proposed the Liu-type shrinkage estimators, namely linear shrinkage, preliminary test, shrinkage preliminary test, Stein-type, and positive Stein-type Liu estimators to estimate the count parameters in the ZINB model, when some of the predictor variables have not a significant effect to predict the response variable so that a sub-model may be sufficient. The asymptotic distributional biases and variances of the proposed estimators are nicely demonstrated. We also compared the performance of the Liu-type shrinkage estimators along with the Liu-type unrestricted estimator by using an extensive Monte Carlo simulation study. The results show that the performances of the proposed estimators are superior to those based on Liu-type unrestricted estimators. We also applied the proposed estimation methods to Expenditure and Default Data.