Bayesian shrinkage approaches to unbalanced problems of estimation and prediction on the basis of negative multinomial samples

In this paper, we treat estimation and prediction problems where negative multinomial variables are observed and, in particular, consider unbalanced settings. First, the problem of estimating multiple parameter vectors under standardized squared error loss is treated a new empirical Bayes estimator which dominates uniformly minimum variance unbiased (UMVU) suitable conditions derived. Next, joint predictive density several tables Kullback–Leibler divergence obtain sufficient condition Bayesian with respect to hierarchical shrinkage prior Jeffreys prior. Finally, our proposed give risk improvements simulations methods applied real data resulting from inverse sampling method.