María Dolores Esteban(University Miguel Hernández of Elche),  María José Lombardía (University of A Coruña), Esther López-Vizcaíno ( Galician Institute of Statistics),   Domingo Morales (University Miguel Hernández of Elche) and Agustín Pérez (University Miguel Hernández of 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.

Keywords.  Labour Force Survey; Area-level models; Compositional data; Bootstrap; Labour status,