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Spatial robust small area estimation

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  • Timo Schmid
  • Ralf Münnich

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. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Timo Schmid & Ralf Münnich, 2014. "Spatial robust small area estimation," Statistical Papers, Springer, vol. 55(3), pages 653-670, August.
  • Handle: RePEc:spr:stpapr:v:55:y:2014:i:3:p:653-670
    DOI: 10.1007/s00362-013-0517-y
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    References listed on IDEAS

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    Cited by:

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    2. Żądło Tomasz, 2020. "On Accuracy Estimation Using Parametric Bootstrap in small Area Prediction Problems," Journal of Official Statistics, Sciendo, vol. 36(2), pages 435-458, June.
    3. Saeideh Kamgar & Florian Meinfelder & Ralf Münnich & Hamidreza Navvabpour, 2020. "Estimation within the new integrated system of household surveys in Germany," Statistical Papers, Springer, vol. 61(5), pages 2091-2117, October.
    4. Jan Pablo Burgard & Joscha Krause & Dennis Kreber & Domingo Morales, 2021. "The generalized equivalence of regularization and min–max robustification in linear mixed models," Statistical Papers, Springer, vol. 62(6), pages 2857-2883, December.
    5. Huapeng Li & Yukun Liu & Riquan Zhang, 2019. "Small area estimation under transformed nested-error regression models," Statistical Papers, Springer, vol. 60(4), pages 1397-1418, August.
    6. Timo Schmid & Nikos Tzavidis & Ralf Münnich & Ray Chambers, 2016. "Outlier Robust Small-Area Estimation Under Spatial Correlation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 806-826, September.
    7. Baldermann, Claudia & Salvati, Nicola & Schmid, Timo, 2016. "Robust small area estimation under spatial non-stationarity," Discussion Papers 2016/5, Free University Berlin, School of Business & Economics.
    8. Schmid, Timo & Tzavidis, Nikos & Münnich, Ralf & Chambers, Ray, 2015. "Outlier robust small area estimation under spatial correlation," Discussion Papers 2015/8, Free University Berlin, School of Business & Economics.

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