Small area estimation of proportions under area-level compositional mixed models
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Small area estimation of proportions under area-level compositional mixed models María Dolores Esteban1 · María José Lombardía2 · Esther López-Vizcaíno3 · Domingo Morales1 · Agustín Pérez1 Received: 6 February 2019 / Accepted: 24 October 2019 © Sociedad de Estadística e Investigación Operativa 2019
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. Keywords Labour Force Survey · Small area estimation · Area-level models · Compositional data · Bootstrap · Labour status Mathematics Subject Classification 62E30 · 62J12
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. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11749019-00688-w) contains supplementary material, which is available to authorized users.
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Agustín Pérez [email protected]
1
Universidad Miguel Hernández de Elche, Alicante, Spain
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CITIC, Universidade da Coruña, A Coruña, Spain
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Instituto Galego de Estatística, Santiago de Compostela, Spain
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M. D. Esteban et al.
1 Introduction Statistical offices are interested on the estimation of socio-economic indicators, like proportions or counts, for the whole population or for subsets called domains. Sampling designs are developed for obtaining precise estimators on their target (planned) domains. Statisticians are also asked to provide estimates for unplanned domains (small areas), where sample sizes are too small to carry out such estimations. Small Area Estimation (SAE) deals with this kind of problems by combining tools of survey sampling and statistical modelling at the unit or at the area level. The monographs of Rao (2003) and of Rao and Molina (2015) give a general description of SAE. In Galicia (north-west of Spain), the Spanish Labour Force Survey (SLFS) provides information about labour market indicators. The territory of Galicia is hierarchically divided into counties and municipalities. As the sampling design of the SLFS is stratified with strata defined by the size of the municipalities and most municipalities are not represented in the sample, the direct estimates at the mu
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