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Small area estimation with spatio-temporal Fay–Herriot models

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  • Marhuenda, Yolanda
  • Molina, Isabel
  • Morales, Domingo

Abstract

Small area estimation is studied under a spatio-temporal Fay–Herriot model. Model fitting based on restricted maximum likelihood is described and empirical best linear unbiased predictors are derived under the model. A parametric bootstrap procedure is proposed for the estimation of the mean squared error of the small area estimators. The spatio-temporal model is compared with simpler models through simulation experiments, analyzing the gain in efficiency achieved by the use of the more complex model. The performance of the parametric bootstrap estimator of the mean squared error is also assessed. An application with Spanish EU-SILC data is carried out to obtain estimates of poverty indicators for Spanish provinces in 2008, making use of survey data from years 2004–2008.

Suggested Citation

  • Marhuenda, Yolanda & Molina, Isabel & Morales, Domingo, 2013. "Small area estimation with spatio-temporal Fay–Herriot models," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 308-325.
    • Handle: RePEc:eee:csdana:v:58:y:2013:i:c:p:308-325
    DOI: 10.1016/j.csda.2012.09.002
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    References listed on IDEAS

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    1. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    2. 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.
    3. González-Manteiga, W. & Lombardi­a, M.J. & Molina, I. & Morales, D. & Santamari­a, L., 2008. "Analytic and bootstrap approximations of prediction errors under a multivariate Fay-Herriot model," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5242-5252, August.
    4. Esteban, M.D. & Morales, D. & Pérez, A. & Santamaría, L., 2012. "Small area estimation of poverty proportions under area-level time models," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2840-2855.
    5. 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.
    6. Guillermo Villa & Isabel Molina & Roland Fried, 2011. "Modeling attendance at Spanish professional football league," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(6), pages 1189-1206, April.
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