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Small area prediction of proportions and counts under a spatial Poisson mixed model

Author

Listed:
  • Miguel Boubeta

    (Universidade da Coruña)

  • María José Lombardía

    (Universidade da Coruña)

  • Domingo Morales

    (Universidad Miguel Hernández de Elche)

Abstract

This paper introduces an area-level Poisson mixed model with SAR(1) spatially correlated random effects. Small area predictors of proportions and counts are derived from the new model and the corresponding mean squared errors are estimated by parametric bootstrap. The behaviour of the introduced predictors is empirically investigated by running model-based simulation experiments. An application to real data from the Spanish living conditions survey of Galicia (Spain) is given. The target is the estimation of domain proportions of women under the poverty line.

Suggested Citation

  • Miguel Boubeta & María José Lombardía & Domingo Morales, 2024. "Small area prediction of proportions and counts under a spatial Poisson mixed model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 33(4), pages 1193-1215, September.
    • Handle: RePEc:spr:stmapp:v:33:y:2024:i:4:d:10.1007_s10260-023-00729-7
    DOI: 10.1007/s10260-023-00729-7
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    References listed on IDEAS

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    1. 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.
    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. Miguel Boubeta & María José Lombardía & Domingo Morales, 2016. "Empirical best prediction under area-level Poisson mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 548-569, September.
    4. S Sugasawa, 2020. "Robust empirical Bayes small area estimation with density power divergence," Biometrika, Biometrika Trust, vol. 107(2), pages 467-480.
    5. Joscha Krause & Jan Pablo Burgard & Domingo Morales, 2022. "Robust prediction of domain compositions from uncertain data using isometric logratio transformations in a penalized multivariate Fay–Herriot model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(1), pages 65-96, February.
    6. Boubeta, Miguel & Lombardía, María José & Morales, Domingo, 2017. "Poisson mixed models for studying the poverty in small areas," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 32-47.
    7. 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.
    8. Chandra, Hukum & Salvati, Nicola & Chambers, Ray & Tzavidis, Nikos, 2012. "Small area estimation under spatial nonstationarity," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2875-2888.
    9. Jiming Jiang & P. Lahiri, 2006. "Mixed model prediction and small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-96, June.
    10. Esther López-Vizcaíno & María José Lombardía & Domingo Morales, 2015. "Small area estimation of labour force indicators under a multinomial model with correlated time and area effects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(3), pages 535-565, June.
    11. 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.
    12. 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.
    13. 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.
    14. Chandra, Hukum & Salvati, Nicola & Chambers, Ray, 2018. "Small area estimation under a spatially non-linear model," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 19-38.
    15. Claudia Baldermann & Nicola Salvati & Timo Schmid, 2018. "Robust Small Area Estimation under Spatial Non†stationarity," International Statistical Review, International Statistical Institute, vol. 86(1), pages 136-159, April.
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