Small area prediction for a unit-level lognormal model

Abstract

Many variables of interest in business and agricultural surveys have skewed distributions. Small area estimation methods are investigated under an assumption that the lognormal model is a reasonable approximation for the distribution of the response given covariates. Closed form expressions for an empirical Bayes (EB) predictor and for the associated mean squared error estimator are derived. In simulation studies, the EB predictors are more efficient than model-based direct and synthetic estimators previously proposed for lognormal data. Also, coverage of confidence intervals for the lognormal predictions approximate the nominal coverage. The simulations also demonstrate that the suggested predictor is robust to departures from the assumptions of the lognormal model. The methodology is successfully applied to estimate erosion rates for hydrologic units using data from the Conservation Effects Assessment Project.