🤖 AI Summary
本文提出了一种结合偏最小二乘法与Fay-Herriot模型的新方法，用于解决高维且高度相关辅助变量集带来的小区域估计问题，并应用于莫桑比克地区人均消费估算。
📝 Abstract
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.