**Sankhya: The Indian Journal of Statistics**

1995, Volume 57, Series B, Pt. 3, pp. 338--352

**NONPARAMETRIC CONSTRAINED BAYES PREDICTION OF MEANS OF FINITE POPULATIONS**

By

RAM C. TIWARI, *University of North Carolina at Charlotte*

and

JYOTI N. ZALKIKAR, *Florida International University*

SUMMARY. Simultaneous estimation of several parameters is widely discussed in the Bayesian context. However as pointed out in Ghosh (1992) in a very general setup, the Bayes estimators overshrink the observed data towards the prior means and this results in similar 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. This idea was first proposed by Louis (1984) in the context of estimation of several normal means with known variances. In this article we utilize this idea in a nonparametric Bayesian setting for prediction of means of finite population 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 th first two moments derived from the histograms from the predictors. The results are applied to the two actual data sets; one borrowed from Ghosh (1992) involving prediction of finite population means along the subgroup analysis and the other taken from Battese, Harter and Fuller (1988) involving small-area prediction under soybean crop.

*AMS (1990) subject classification.* 62G05, 62C10.

*Key words and phrases*. Asymptotic optimality, Dirichlet process, Empirical Bayes.