Smoothing and Benchmarking for Small Area Estimation. (16th March 2020)

• Record Type: Journal Article
• Authors: Steorts, Rebecca C.; Schmid, Timo; Tzavidis, Nikos
• Is Part Of: International statistical review. Volume 88:Number 3(2020)
• Page Start: 580
• Page End: 598
• Publication Date: 2020-03-16
• Subjects: benchmarking -- decision theory -- small area estimation -- web‐scraped data; Statistics -- Periodicals; Statistics -- Bibliography -- Periodicals; Statistics -- Bibliography; Statistics -- Periodicals; Statistique; Statistique -- Périodiques; Statistique -- Bibliographie -- Périodiques; Statistique -- Étude et enseignement -- Périodiques; Statistique -- Étude et enseignement -- Bibliographie -- Périodiques; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519.2
• DOI: 10.1111/insr.12373
• Languages: English
• ISSNs: 0306-7734

Abstract

Summary: Small area estimation is concerned with methodology for estimating population parameters associated with a geographic area defined by a cross‐classification that may also include non‐geographic dimensions. In this paper, we develop constrained 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. The constrained estimators are the solutions to tractable optimisation problems and have closed‐form solutions. Mean squared errors of the constrained estimators are calculated via bootstrapping. Our approach assumes the Bayes estimator exists and is applicable to any proposed model. In addition, we give special cases of our techniques under certain distributional assumptions. We illustrate the proposed methodology using web‐scraped data on Berlin rents aggregated over areas to ensure privacy.