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Smoothing and Benchmarking for Small Area Estimation

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  • Rebecca C. Steorts
  • Timo Schmid
  • Nikos Tzavidis

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.

Suggested Citation

  • Rebecca C. Steorts & Timo Schmid & Nikos Tzavidis, 2020. "Smoothing and Benchmarking for Small Area Estimation," International Statistical Review, International Statistical Institute, vol. 88(3), pages 580-598, December.
    • Handle: RePEc:bla:istatr:v:88:y:2020:i:3:p:580-598
    DOI: 10.1111/insr.12373
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    References listed on IDEAS

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    1. G. Datta & M. Ghosh & R. Steorts & J. Maples, 2011. "Bayesian benchmarking with applications to small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 574-588, November.
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    3. Nikos Tzavidis & Li‐Chun Zhang & Angela Luna & Timo Schmid & Natalia Rojas‐Perilla, 2018. "From start to finish: a framework for the production of small area official statistics," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 927-979, October.
    4. Lee, Ann B. & Wasserman, Larry, 2010. "Spectral Connectivity Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1241-1255.
    5. W. R. Bell & G. S. Datta & M. Ghosh, 2013. "Benchmarking small area estimators," Biometrika, Biometrika Trust, vol. 100(1), pages 189-202.
    6. Isabel Molina & Nicola Salvati & Monica Pratesi, 2009. "Bootstrap for estimating the MSE of the Spatial EBLUP," Computational Statistics, Springer, vol. 24(3), pages 441-458, August.
    7. Monica Pratesi & Nicola Salvati, 2008. "Small area estimation: the EBLUP estimator based on spatially correlated random area effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(1), pages 113-141, February.
    8. Malay Ghosh & Rebecca Steorts, 2013. "Two-stage benchmarking as applied to small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(4), pages 670-687, November.
    9. J. D. Opsomer & G. Claeskens & M. G. Ranalli & G. Kauermann & F. J. Breidt, 2008. "Non‐parametric small area estimation using penalized spline regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 265-286, February.
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    Cited by:

    1. Nandram, Balgobin & Cruze, Nathan B & Erciulescu, Andreea L & Chen, Lu, 2022. "Bayesian Small Area Models under Inequality Constraints with Benchmarking and Double Shrinkage," NASS Research Reports 327250, United States Department of Agriculture, National Agricultural Statistics Service.

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