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arXiv · 1410.7056

Smoothing, Clustering, and Benchmarking for Small Area Estimation

Rebecca C. Steorts
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Abstract

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.

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Rebecca C. Steorts. 2014-10-26. Smoothing, Clustering, and Benchmarking for Small Area Estimation. https://arxiv.org/abs/1410.7056

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