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Time stable empirical best predictors under a unit-level model

Author

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  • Guadarrama, María
  • Morales, Domingo
  • Molina, Isabel

Abstract

Comparability as well as stability over time are highly desirable properties of regularly published statistics, specially when they are related to important issues such as people’s living conditions. For instance, poverty statistics displaying drastic changes from one period to the next for the same area have low credibility. In fact, longitudinal surveys that collect information on the same phenomena at several time points are indeed very popular, specially because they allow analyzing changes over time. Data coming from those surveys are likely to present correlation over time, which should be accounted for by the considered statistical procedures, and methods that account for it are expected to yield more stable estimates over time. A unit-level temporal linear mixed model is considered for small area estimation using historical information. The proposed model includes random time effects nested within the usual area effects, following an autoregressive process of order 1, AR(1). Based on the proposed model, empirical best predictors (EBPs) of small area parameters that are comparable for different time points and are expected to be more stable are derived. Explicit expressions are provided for the EBPs of some common poverty indicators. A parametric bootstrap method is also proposed for estimation of the mean square errors under the model. The proposed methods are studied through different simulation experiments, and are illustrated in an application to poverty mapping in Spanish provinces using survey data on living conditions from years 2004–2006.

Suggested Citation

  • Guadarrama, María & Morales, Domingo & Molina, Isabel, 2021. "Time stable empirical best predictors under a unit-level model," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    • Handle: RePEc:eee:csdana:v:160:y:2021:i:c:s0167947321000608
    DOI: 10.1016/j.csda.2021.107226
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    References listed on IDEAS

    as
    1. 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.
    2. María Guadarrama & Isabel Molina & J. N. K. Rao, 2016. "A Comparison Of Small Area Estimation Methods For Poverty Mapping," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 41-66, March.
    3. Mamadou S. Diallo & J. N. K. Rao, 2018. "Small area estimation of complex parameters under unit‐level models with skew‐normal errors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(4), pages 1092-1116, December.
    4. Yolanda Marhuenda & Isabel Molina & Domingo Morales & J. N. K. Rao, 2017. "Poverty mapping in small areas under a twofold nested error regression model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1111-1136, October.
    5. 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.
    6. repec:csb:stintr:v:17:y:2016:i:1:p:41-66 is not listed on IDEAS
    7. Tomáš Hobza & Domingo Morales & Laureano Santamaría, 2018. "Small area estimation of poverty proportions under unit-level temporal binomial-logit mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 270-294, June.
    8. 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.
    9. 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.
    10. Molina, Isabel, 2019. "Desagregación de datos en encuestas de hogares: metodologías de estimación en áreas pequeñas," Estudios Estadísticos 44214, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    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. Natalia Rojas‐Perilla & Sören Pannier & Timo Schmid & Nikos Tzavidis, 2020. "Data‐driven transformations in small area estimation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 121-148, January.
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