2014/10/26 by Rebecca C. Steorts, Steorts, Rebecca C.
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Applications (stat.AP) #Economic and Environmental Valuation #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #demographic modeling and climate adaptation
paper · pdf · doi:10.48550/arxiv.1410.7056
openalex publication_date 2014/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.