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<p>Developing data-driven models is an active field in small area estimation, while no such research has yet explored areal compositional proportions. In this paper, we summarize and extend flexible compositional parametric transformations and propose two classes of models under the empirical Bayes framework: the compositional transformed multivariate Fay-Herriot model and the compositional transformed folded multivariate Fay-Herriot model. The empirical Bayes estimation is based on Aitchison squared loss, and evaluation measures are defined under Aitchison geometry. The performance of the models and estimators is validated through simulations. Finally, proposed models are applied to the National Survey of Occupation and Employment (ENOE) data, exploring municipal employment status proportions in northern Mexico under complex survey designs.</p>

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Data-driven small area estimation for compositional proportions based on parametric transformations

  • 期刊论文

  • 发表日期：

    2026年7月29日

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  • Xucheng Wang,
  • Lichao Yu,
  • Hanjun Yu

摘要

Developing data-driven models is an active field in small area estimation, while no such research has yet explored areal compositional proportions. In this paper, we summarize and extend flexible compositional parametric transformations and propose two classes of models under the empirical Bayes framework: the compositional transformed multivariate Fay-Herriot model and the compositional transformed folded multivariate Fay-Herriot model. The empirical Bayes estimation is based on Aitchison squared loss, and evaluation measures are defined under Aitchison geometry. The performance of the models and estimators is validated through simulations. Finally, proposed models are applied to the National Survey of Occupation and Employment (ENOE) data, exploring municipal employment status proportions in northern Mexico under complex survey designs.