Assessing regional population compositions is an important task in many research fields. Small area estimation with generalized linear mixed models marks a powerful tool for this purpose. However, the method has limitations in practice. When the data are subject to measurement errors, small area models produce inefficient or biased results since they cannot account for data uncertainty. This is particularly problematic for composition prediction, since generalized linear mixed models often rely on approximate likelihood inference. Obtained predictions are not reliable. We propose a robust multivariate Fay–Herriot model to solve these issues. It combines compositional data analysis with robust optimization theory. The nonlinear estimation of compositions is restated as a linear problem through isometric logratio transformations. Robust model parameter estimation is performed via penalized maximum likelihood. A robust best predictor is derived. Simulations are conducted to demonstrate the effectiveness of the approach. An application to alcohol consumption in Germany is provided.

中文翻译：

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在惩罚多元 Fay-Herriot 模型中使用等距对数比变换对不确定数据中的域组成进行稳健预测

评估区域人口构成是许多研究领域的一项重要任务。使用广义线性混合模型进行小面积估计是实现此目的的有力工具。然而，该方法在实践中存在局限性。当数据受到测量误差的影响时，小面积模型会产生低效或有偏差的结果，因为它们无法解释数据的不确定性。这对于成分预测尤其成问题，因为广义线性混合模型通常依赖于近似似然推断。获得的预测不可靠。我们提出了一个稳健的多元 Fay-Herriot 模型来解决这些问题。它将成分数据分析与稳健的优化理论相结合。通过等距对数比变换将成分的非线性估计重新表述为线性问题。稳健的模型参数估计是通过惩罚最大似然来执行的。导出了一个稳健的最佳预测器。进行模拟以证明该方法的有效性。提供了在德国饮酒的应用程序。