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Small area estimation of proportions under area-level compositional mixed models

Author

Listed:
  • María Dolores Esteban

    (Universidad Miguel Hernández de Elche)

  • María José Lombardía

    (Universidade da Coruña)

  • Esther López-Vizcaíno

    (Instituto Galego de Estatística)

  • Domingo Morales

    (Universidad Miguel Hernández de Elche)

  • Agustín Pérez

    (Universidad Miguel Hernández de Elche)

Abstract

This paper introduces area-level compositional mixed models by applying transformations to a multivariate Fay–Herriot model. Small area estimators of the proportions of the categories of a classification variable are derived from the new model, and the corresponding mean squared errors are estimated by parametric bootstrap. Several simulation experiments designed to analyse the behaviour of the introduced estimators are carried out. An application to real data from the Spanish Labour Force Survey of Galicia (north-west of Spain), in the first quarter of 2017, is given. The target is the estimation of domain proportions of people in the four categories of the variable labour status: under 16 years, employed, unemployed and inactive.

Suggested Citation

  • María Dolores Esteban & María José Lombardía & Esther López-Vizcaíno & Domingo Morales & Agustín Pérez, 2020. "Small area estimation of proportions under area-level compositional mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 793-818, September.
    • Handle: RePEc:spr:testjl:v:29:y:2020:i:3:d:10.1007_s11749-019-00688-w
    DOI: 10.1007/s11749-019-00688-w
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    References listed on IDEAS

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    1. Gonzalez-Manteiga, W. & Lombardia, M.J. & Molina, I. & Morales, D. & Santamaria, L., 2007. "Estimation of the mean squared error of predictors of small area linear parameters under a logistic mixed model," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2720-2733, February.
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    8. 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.
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    10. 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.
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    14. Ray Chambers & Nicola Salvati & Nikos Tzavidis, 2016. "Semiparametric small area estimation for binary outcomes with application to unemployment estimation for local authorities in the UK," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(2), pages 453-479, February.
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