Smoothing, Clustering, and Benchmarking for Small Area Estimation

TL;DR

This paper introduces constrained Bayesian estimation methods for small area estimation that incorporate smoothness, clustering, and benchmarking constraints, providing tractable solutions with broad applicability and no distributional assumptions.

Contribution

It develops a unified framework for constrained Bayesian estimation in small area problems, including geometric interpretation and closed-form solutions.

Findings

Methods are applicable to linear and non-linear estimators.

Techniques are distribution-free and versatile.

Demonstrated on U.S. Census data.

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.