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Benchmarking small area estimators

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  • W. R. Bell
  • G. S. Datta
  • M. Ghosh

Abstract

This paper considers benchmarking issues in the context of small area estimation. We find optimal estimators within the class of benchmarked linear estimators under linear constraints. This extends existing results for external and internal benchmarking, and also links the two. Necessary and sufficient conditions for self-benchmarking are found for an augmented model. Most results of this paper are found using ideas of orthogonal projection Copyright 2013, Oxford University Press.

Suggested Citation

  • W. R. Bell & G. S. Datta & M. Ghosh, 2013. "Benchmarking small area estimators," Biometrika, Biometrika Trust, vol. 100(1), pages 189-202.
    • Handle: RePEc:oup:biomet:v:100:y:2013:i:1:p:189-202
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    File URL: http://hdl.handle.net/10.1093/biomet/ass063
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    Citations

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    Cited by:

    1. 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.
    2. Malay Ghosh & Tatsuya Kubokawa & Yuki Kawakubo, 2014. "Benchmarked Empirical Bayes Methods in Multiplicative Area-level Models with Risk Evaluation," CIRJE F-Series CIRJE-F-918, CIRJE, Faculty of Economics, University of Tokyo.
    3. Ghosh Malay, 2020. "Small area estimation: its evolution in five decades," Statistics in Transition New Series, Statistics Poland, vol. 21(4), pages 1-22, August.
    4. Marius Stefan & Michael Hidiroglou, 2021. "Benchmarked Estimators for a Small Area Mean Under a Onefold Nested Regression Model," International Statistical Review, International Statistical Institute, vol. 89(1), pages 108-131, April.
    5. Malay Ghosh, 2020. "Small area estimation: its evolution in five decades," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 1-22, August.
    6. Maria Rosaria Ferrante & Silvia Pacei, 2017. "Small domain estimation of business statistics by using multivariate skew normal models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1057-1088, October.
    7. Zhang Junni L. & Bryant John, 2020. "Fully Bayesian Benchmarking of Small Area Estimation Models," Journal of Official Statistics, Sciendo, vol. 36(1), pages 197-223, March.
    8. Benavent, Roberto & Morales, Domingo, 2016. "Multivariate Fay–Herriot models for small area estimation," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 372-390.
    9. Arthur Acolin & Ari Decter-Frain & Matt Hall, 2022. "Small-area estimates from consumer trace data," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 47(27), pages 843-882.
    10. Rebecca Steorts & M. Ugarte, 2014. "Comments on: “Single and two-stage cross-sectional and time series benchmarking procedures for small area estimation”," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 680-685, December.
    11. Ryan Janicki & Andrew Vesper, 2017. "Benchmarking techniques for reconciling Bayesian small area models at distinct geographic levels," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 557-581, November.

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