Combining survey and auxiliary data to produce official statistics is gaining interest at federal agencies and among policy makers due to its efficiency. Recent studies have shown the practicality of small area estimation modeling approaches in the context of integrating data from multiple sources to improve estimation at fine levels of aggregation. In this article, agricultural predictions are constructed using a hierarchical Bayes subarea-level model, fit to data available from different sources. Auxiliary data are initially used to complement the survey data and define the prediction space, and then to define covariates for the model. Finally, not-in-sample predictions are constructed using the model output, and benchmarking constraints are imposed on the final set of in-sample and not-in-sample predictions. Unlike most of the studies discussing not-in-sample prediction, this article illustrates a method that uses the data available from multiple sources to define the prediction space. As a consequence, the resulting framework provides a larger set of nationwide predictions as candidate for official statistics, and extrapolation is not of concern. Challenges in developing the methods to combine different data sources are discussed in the context of planted acreage prediction.

Given a sample from a finite population, we provide a nonparametric Bayesian prediction interval for a finite population mean when a standard normal assumption may be tenuous. We will do so using a Dirichlet process (DP), a nonparametric Bayesian procedure which is currently receiving much attention. An asymptotic Bayesian prediction interval is well known but it does not incorporate all the features of the DP. We show how to compute the exact prediction interval under the full Bayesian DP model. However, under the DP, when the population size is much larger than the sample size, the computational task becomes expensive. Therefore, for simplicity one might still want to consider useful and accurate approximations to the prediction interval. For this purpose, we provide a Bayesian procedure which approximates the distribution using the exchangeability property (correlation) of the DP together with normality. We compare the exact interval and our approximate interval with three standard intervals, namely the design-based interval under simple random sampling, an empirical Bayes interval and a moment-based interval which uses the mean and variance under the DP. However, these latter three intervals do not fully utilize the posterior distribution of the finite population mean under the DP. Using several numerical examples and a simulation study we show that our approximate Bayesian interval is a good competitor to the exact Bayesian interval for different combinations of sample sizes and population sizes.