Improved shrinkage estimators in zero-inflated negative binomial regression model

Zero-inflated negative binomial model is an appropriate choice to model count response variables with excessive zeros and overdispersion simultaneously. This paper addressed parameter estimation in the zero-inflated negative binomial model when there are many predictors, so that some of them are inactive and have not influence on the response variable. We proposed parameter estimation based on the linear shrinkage, pretest, shrinkage pretest, Stein-type, and positive Stein-type estimators. We obtained the asymptotic distributional biases and risks of the suggested estimators theoretically. We also conducted a Monte Carlo simulation study to compare the performance of each estimator with the unrestricted estimator in terms of simulated relative efficiency. Based on the results, the performances of the proposed estimators were better than that of the unrestricted estimator. The suggested estimators were applied to the wildlife fish data to appraise their performance.