发表机构
University of Pisa; Catholic University of the Sacred Heart（比萨大学; 圣心天主教大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出将偏最小二乘法融入Fay-Herriot模型的部分Fay-Herriot估计器，用于高维相关辅助变量下的小域估计，并在莫桑比克区级消费估算中验证了其更低的均方误差和更好的预测性能。
AI 中文摘要
本文提出了一种新的小域估计方法，将偏最小二乘法整合到Fay-Herriot模型中，以应对高维且高度相关的辅助变量集所带来的挑战。由此产生的部分Fay-Herriot（PFH）估计器构建了与目标变量关联最大化的监督成分，增强了模型的稳定性和预测效率。蒙特卡洛模拟表明，PFH估计器比标准Fay-Herriot估计器实现了更低的均方误差，并且在依赖更少潜在维度的同时优于基于主成分的替代方法。该方法被应用于估算莫桑比克区级人均消费，其中调查数据源由大量相关的普查变量补充。所得估计结果突显了显著的地理异质性，并揭示了贫困的空间聚集。总体而言，研究结果表明，所提出的监督降维方法是在高维背景下生成可靠指标的有效且易于解释的工具。
英文摘要
This paper proposes a new small area estimation approach that integrates Partial Least Squares within the Fay-Herriot model to address the challenges posed by high-dimensional and highly correlated auxiliary variables sets. The resulting Partial Fay-Herriot (PFH) estimator constructs supervised components that maximize their association with the target variable, enhancing model stability and predictive efficiency. Monte Carlo simulations demonstrate that PFH estimator achieves lower mean squared error than the standard Fay-Herriot estimator and outperforms principal components-based alternatives while relying on fewer latent dimensions. The methodology is applied to the estimation of district-level per capita consumption in Mozambique, where the survey data source is complemented by large set of correlated census variables. The resulting estimates highlight pronounced geographic heterogeneity and uncover spatial clusters of deprivation. Overall, the findings show that the proposed supervised dimension-reduction approach represents an effective and easily interpretable tool for producing reliable indicators in high-dimensional contexts.
