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

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.

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Correspondence to Agustín Pérez.

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Supported by the Instituto Galego de Estatística, by the grants PGC2018-096840-B-I00 and MTM2017-82724-R of the Spanish Ministerio de Economía y Competitividad and by the Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2016-015 and Centro Singular de Investigación de Galicia ED431G/01), all of them through the ERDF.

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Esteban, M.D., Lombardía, M.J., López-Vizcaíno, E. et al. Small area estimation of proportions under area-level compositional mixed models. TEST 29, 793–818 (2020). https://doi.org/10.1007/s11749-019-00688-w

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Keywords

  • Labour Force Survey
  • Small area estimation
  • Area-level models
  • Compositional data
  • Bootstrap
  • Labour status

Mathematics Subject Classification

  • 62E30
  • 62J12