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Small area estimation of average compositions under multivariate nested error regression models

Author

Listed:
  • María Dolores Esteban

    (Universidad Miguel Hernández de Elche)

  • María José Lombardía

    (Universidade da Coruña, CITIC)

  • Esther López-Vizcaíno

    (Instituto Galego de Estatística)

  • Domingo Morales

    (Universidad Miguel Hernández de Elche)

  • Agustín Pérez

    (Universidad Miguel Hernández de Elche)

Abstract

This paper investigates the small area estimation of population averages of unit-level compositional data. The new methodology transforms the compositions into vectors of $$R^m$$ R m and assumes that the vectors follow a multivariate nested error regression model. Empirical best predictors of domain indicators are derived from the fitted model, and their mean squared errors are estimated by parametric bootstrap. The empirical analysis of the behavior of the introduced predictors is investigated by means of simulation experiments. An application to real data from the Spanish household budget survey is given. The target is to estimate the average of proportions of annual household expenditures on food, housing and others, by Spanish provinces.

Suggested Citation

  • María Dolores Esteban & María José Lombardía & Esther López-Vizcaíno & Domingo Morales & Agustín Pérez, 2023. "Small area estimation of average compositions under multivariate nested error regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 651-676, June.
    • Handle: RePEc:spr:testjl:v:32:y:2023:i:2:d:10.1007_s11749-023-00847-0
    DOI: 10.1007/s11749-023-00847-0
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    8. 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.
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