Smoothing and benchmarking for small area estimation
Smoothing and benchmarking for small area estimation
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.
benchmarking, decision theory, small area estimation, web-scraped data
580-598
Steorts, Rebecca
b9710d75-99a3-4baf-b372-2d3dd6175913
Schmid, Timo
6337d53e-bfc0-4a18-b31c-551d2f859336
Tzavidis, Nikolaos
431ec55d-c147-466d-9c65-0f377b0c1f6a
1 December 2020
Steorts, Rebecca
b9710d75-99a3-4baf-b372-2d3dd6175913
Schmid, Timo
6337d53e-bfc0-4a18-b31c-551d2f859336
Tzavidis, Nikolaos
431ec55d-c147-466d-9c65-0f377b0c1f6a
Steorts, Rebecca, Schmid, Timo and Tzavidis, Nikolaos
(2020)
Smoothing and benchmarking for small area estimation.
International Statistical Review, 88 (3), .
(doi:10.1111/insr.12373).
Abstract
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.
Text
Smoothing Tzavidis
- Accepted Manuscript
More information
Accepted/In Press date: 17 February 2020
e-pub ahead of print date: 16 March 2020
Published date: 1 December 2020
Additional Information:
Funding Information:
Schmid and Tzavidis are supported by ES/N011619/1 — Innovations in Small Area Estimation Methodologies from the UK Economic and Social Research Council. Tzavidis is also supported by the InGRID 2 EU‐Horizon 2020 infrastructure grant ( http://www.inclusivegrowth.eu ). The authors thank Empirica‐Systeme GmbH (www.empirica‐systeme.de) for providing the data set used in the application. The ideas of this paper are of the authors and not of the funding organisations or the data providers. Finally, the authors thank the Editor and the reviewers for comments that significantly improved the paper. The authors also thank David Banks for providing minor comments regarding manuscript.
Publisher Copyright:
© 2020 The Authors. International Statistical Review © 2020 International Statistical Institute
Keywords:
benchmarking, decision theory, small area estimation, web-scraped data
Identifiers
Local EPrints ID: 438354
URI: http://eprints.soton.ac.uk/id/eprint/438354
ISSN: 0306-7734
PURE UUID: e11c146c-bede-4056-9979-b20fd18cbcb0
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Date deposited: 06 Mar 2020 17:33
Last modified: 17 Mar 2024 05:24
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Contributors
Author:
Rebecca Steorts
Author:
Timo Schmid
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