Summary: Simultaneous estimation of several parameters is widely discussed in the Bayesian context. However, the Bayes estimators overshrink the observed data towards the prior means and this results in smaller sample variance of the Bayes estimators ensemble compared to the posterior expectation of the sample variance of the unobserved parameters ensemble under the prior. It is often desirable to correct this problem by matching the first two moments from the histogram of the parameters.
We utilize this idea in a nonparametric Bayesian setting for prediction of means of finite populations. In this approach, the different finite populations are assumed to be independent realizations from independent superpopulations having Dirichlet process priors. Nonparametric Bayes and empirical Bayes predictors are derived under the constraints on the first two moments derived from the histogram of the predictors. The results are applied to two actual data sets; one involving prediction of finite population means along with subgroup analysis and the other involving small-area prediction under soybean crop.