Smoothing, Clustering, and Benchmarking for Small Area Estimation

We develop constrained Bayesian estimation methods for small area problems: those requiring smoothness with respect to similarity across areas, such as geographic proximity or clustering by covariates; and benchmarking constraints, requiring (weighted) means of estimates to agree across levels of aggregation. We develop methods for constrained estimation decision-theoretically and discuss their geometric interpretation. Our constrained estimators are the solutions to tractable optimization problems and have closed-form solutions. Mean squared errors of the constrained estimators are calculated via bootstrapping. Our techniques are free of distributional assumptions and apply whether the estimator is linear or non-linear, univariate or multivariate. We illustrate our methods using data from the U.S. Census's Small Area Income and Poverty Estimates program.