Small area prediction for a unit-level lognormal model

Many variables of interest in business and agricultural surveys have skewed distributions. An example from the National Agricultural Statistics Service is the acres harvested for a particular crop. We investigate small area estimation methods for skewed data under the assumption that a lognormal model is a reasonable approximation for the distribution of the response given covariates. Empirical Bayes (EB) predictors and estimators of the mean squared error of the predictors are proposed. In simulation studies, the EB predictors are more efficient than a direct estimator and more efficient than a synthetic estimator.