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Spatial robust small area estimation

Abstract

The accuracy of recent applications in small area statistics in many cases highly depends on the assumed properties of the underlying models and the availability of micro information. In finite population sampling, small sample sizes may increase the sensitivity of the modeling with respect to single units. In these cases, area-specific sample sizes tend to be small such that normal assumptions, even of area means, seem to be violated. Hence, applying robust estimation methods is expected to yield more reliable results. In general, two robust small area methods are applied, the robust EBLUP and the M-quantile method. Additionally, the use of adequate auxiliary information may further increase the accuracy of the estimates. In prediction based approaches where information is needed on universe level, in general, only few variables are available which can be used for modeling. In addition to variables from the dataset, in many cases further information may be available, e.g. geographical information which could indicate spatial dependencies between neighboring areas. This spatial information can be included in the modeling using spatially correlated area effects. Within the paper the classical robust EBLUP is extended to cover spatial area effects via a simultaneous autoregressive model. The performance of the different estimators are compared in a model-based simulation study.

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Acknowledgments

The research was conducted within the BLUE-ETS research project which is funded by the European Commission within the 7th Framework Programme. For more information on the project, we refer to the project page http://www.blue-ets.eu. The first author was supported by the Foundation of German Economy. The authors are grateful to the SAMPLE project (http://www.sample-project.eu/) and Chambers et al. (2013) for providing R-code used in the simulations in this paper. The authors would like to thank the Editor-in-Chief and two anonymous referees for their very valuable comments which helped to improve the paper.

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Correspondence to Timo Schmid.

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Schmid, T., Münnich, R.T. Spatial robust small area estimation. Stat Papers 55, 653–670 (2014). https://doi.org/10.1007/s00362-013-0517-y

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  • DOI: https://doi.org/10.1007/s00362-013-0517-y

Keywords

  • Small area estimation
  • M-quantile
  • Robust EBLUP
  • Spatial correlation

Mathematics subject classification (2000)

  • 62F10
  • 62F35