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Analytic and bootstrap approximations of prediction errors under a multivariate Fay-Herriot model

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  • González-Manteiga, W.
  • Lombardi­a, M.J.
  • Molina, I.
  • Morales, D.
  • Santamari­a, L.

Abstract

The prediction of vectors of small area quantities based on a multivariate Fay-Herriot model is addressed. For this, an empirical best linear unbiased predictor (EBLUP) of the target vector is used, where the model parameters are estimated by two different methods based on moments. The mean cross product error matrix of the multidimensional EBLUP is approximated both analytically and by a wild bootstrap method that yields direct and bias-corrected bootstrap estimators. A simulation study compares the small sample properties of the bootstrap estimators and the analytical approximation, including a comparison under lack of normality. Finally, the number of replicates needed for the bootstrap procedures to get stabilized are studied.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:12:p:5242-5252
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    References listed on IDEAS

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    1. Peter Hall & Tapabrata Maiti, 2006. "On parametric bootstrap methods for small area prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 221-238, April.
    2. Danny Pfeffermann & Richard Tiller, 2005. "Bootstrap Approximation to Prediction MSE for State–Space Models with Estimated Parameters," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 893-916, November.
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    Cited by:

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    3. Marcin Szymkowiak & Andrzej Młodak & Łukasz Wawrowski, 2017. "Mapping Poverty At The Level Of Subregions In Poland Using Indirect Estimation," Statistics in Transition New Series, Polish Statistical Association, vol. 18(4), pages 609-635, December.
    4. Burgard, Jan Pablo & Münnich, Ralf T., 2012. "Modelling over and undercounts for design-based Monte Carlo studies in small area estimation: An application to the German register-assisted census," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2856-2863.
    5. Ugarte, M.D. & Goicoa, T. & Militino, A.F. & Durbán, M., 2009. "Spline smoothing in small area trend estimation and forecasting," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3616-3629, August.
    6. Schmid, Timo & Bruckschen, Fabian & Salvati, Nicola & Zbiranski, Till, 2016. "Constructing socio-demographic indicators for National Statistical Institutes using mobile phone data: Estimating literacy rates in Senegal," Discussion Papers 2016/9, Free University Berlin, School of Business & Economics.
    7. Monique Graf & J. Miguel Marín & Isabel Molina, 2019. "A generalized mixed model for skewed distributions applied to small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 565-597, June.
    8. Walter, Paul & Groß, Markus & Schmid, Timo & Tzavidis, Nikos, 2017. "Estimation of linear and non-linear indicators using interval censored income data," Discussion Papers 2017/22, Free University Berlin, School of Business & Economics.
    9. Jan Pablo Burgard & Joscha Krause & Domingo Morales, 2022. "A measurement error Rao–Yu model for regional prevalence estimation over time using uncertain data obtained from dependent survey estimates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 204-234, March.
    10. Isabel Molina & Ewa Strzalkowska‐Kominiak, 2020. "Estimation of proportions in small areas: application to the labour force using the Swiss Census Structural Survey," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 281-310, January.
    11. 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.
    12. Roberto Benavent & Domingo Morales, 2021. "Small area estimation under a temporal bivariate area-level linear mixed model with independent time effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 195-222, March.
    13. Jan Pablo Burgard & María Dolores Esteban & Domingo Morales & Agustín Pérez, 2021. "Small area estimation under a measurement error bivariate Fay–Herriot model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 79-108, March.
    14. 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.
    15. Dehnel Grażyna & Wawrowski Łukasz, 2020. "Robust estimation of wages in small enterprises: the application to Poland’s districts," Statistics in Transition New Series, Polish Statistical Association, vol. 21(1), pages 137-157, March.
    16. Andreea L. Erciulescu & Jean D. Opsomer, 2022. "A model‐based approach to predict employee compensation components," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1503-1520, November.
    17. Benavent, Roberto & Morales, Domingo, 2016. "Multivariate Fay–Herriot models for small area estimation," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 372-390.
    18. María José Lombardía & Esther López-Vizcaíno & Cristina Rueda, 2021. "Selection model for domains across time: application to labour force survey by economic activities," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 228-254, March.
    19. Angelo Moretti & Natalie Shlomo & Joseph W. Sakshaug, 2020. "Multivariate Small Area Estimation of Multidimensional Latent Economic Well‐being Indicators," International Statistical Review, International Statistical Institute, vol. 88(1), pages 1-28, April.
    20. Grażyna Dehnel & Łukasz Wawrowski, 2020. "Robust estimation of wages in small enterprises: the application to Poland’s districts," Statistics in Transition New Series, Polish Statistical Association, vol. 21(1), pages 137-157, March.
    21. Szymkowiak Marcin & Młodak Andrzej & Wawrowski Łukasz, 2017. "Mapping Poverty at the Level of Subregions in Poland Using Indirect Estimation," Statistics in Transition New Series, Polish Statistical Association, vol. 18(4), pages 609-635, December.
    22. 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.
    23. Jan Pablo Burgard & Domingo Morales & Anna-Lena Wölwer, 2022. "Small area estimation of socioeconomic indicators for sampled and unsampled domains," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 287-314, June.

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