Area-Level Dirichlet Mixed Models for Small Area Estimation of Compositional Data

E. Cabello García, M. D. Esteban Lelfer, T. Hobza, D. Morales González, A. Pérez Martín

A multivariate, area-level model based on the Dirichlet distribution is proposed for estimating compositional indicators in small areas. The direct estimators of the domain category proportions are used as target variables, modelling them directly on the standard simplex. Based on this framework, predictors of proportions, totals, and rates are derived, and their mean squared errors are estimated via parametric bootstrap. Two fitting algorithms are proposed and evaluated through a simulation study. These experiments also study the performance of the new predictors against alternative area-level models and validate the bootstrap procedure. Finally, an application to real data from the Spanish Labour Force Survey (Q4 2022) is presented. The goal is the estimation of employment, unemployment, and inactivity proportions—as well as unemployment rates—disaggregated by province, sex, and age group.

Palabras clave: Labour Force Survey, Small Area Estimation, Dirichlet mixed models, area- level models, compositional data, bootstrap

SI Estimación en áreas pequeñas
4 de septiembre de 2026  11:10
Aula 21

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