Estimation of Fixed Parameters in Negative Binomial Mixed Model Using Shrinkage Estimators

‎In this paper‎, ‎we consider the problem of parameter estimation in {color{blue} negative binomial mixed model} when it is suspected that some of the fixed parameters may be restricted to a subspace via linear shrinkage‎, ‎{color{blue} preliminary test}‎, ‎shrinkage {color{blue} preliminary test}‎, ‎shrinkage‎, ‎and positive shrinkage estimators along with the unrestricted maximum likelihood and restricted estimators‎. ‎The random effects are considered as nuisance parameters‎. ‎We conduct a Monte Carlo simulation study to evaluate the performance of each estimator in the sense of simulated relative efficiency‎. ‎The results of simulation study reveal that the proposed estimation strategies perform more better than {color{blue} the} maximum likelihood method‎. ‎The proposed estimators are applied to a real dataset to appraise their performance‎.