Using shrinkage strategies to estimate fixed effects in zero-inflated negative binomial mixed model

In this paper, we address the estimation of fixed effects parameters in the zero-inflated negative binomial mixed model based on shrinkage estimators, namely linear shrinkage, pretest, shrinkage pretest, shrinkage, and positive-shrinkage estimators when the random effects are considered as nuisance parameters. We compare the performance of the shrinkage estimators to unrestricted and restricted estimators when certain prior subspace information is available. The asymptotic distributional biases and risks of the proposed estimators are obtained. We also conduct a Monte Carlo simulation study to compare the performance of each estimator in the sense of simulated relative efficiency. The results of simulation study show that the proposed estimation strategies perform strongly better than the maximum likelihood method. Finally, proposed methodologies are applied to a real dataset to appraise their performances.