Small area estimation (SAE) plays a central role in survey statistics and epidemiology, providing reliable estimates for domains with limited sample sizes. The multivariate Fay-Herriot model has been extensively used for this purpose, because it enhances estimation accuracy by borrowing strength across multiple correlated variables. In this paper, we develop a Bayesian extension of the multivariate Fay-Herriot model that enables flexible, component-specific shrinkage of the random effects. The proposed approach employs global-local priors formulated through a sandwich mixture representation, allowing adaptive regularization of each element of the random-effect vectors. This construction yields greater robustness and prevents excessive shrinkage in areas exhibiting strong underlying signals. In addition, we incorporate spatial dependence into the model to account for geographical correlation across small areas. The resulting spatial multivariate framework simultaneously exploits cross-variable relationships and spatial structure, yielding improved estimation efficiency. The utility of the proposed method is demonstrated through simulation studies and an empirical application to real survey data.

翻译：小域估计在调查统计与流行病学中具有核心地位，可为样本量有限的域提供可靠估计。多元Fay-Herriot模型因此被广泛使用，因其能通过多个相关变量间借力提升估计精度。本文提出一种多元Fay-Herriot模型的贝叶斯扩展，实现对随机效应各分量的灵活收缩。所提方法采用通过夹层混合表示构建的全局-局部先验，允许对随机效应向量的每个元素进行自适应正则化。该构造具有更强的稳健性，并能防止在具有强潜在信号的区域产生过度收缩。此外，我们在模型中引入空间依赖性以刻画小域间的地理相关性。最终形成的空间多元框架能同时利用跨变量关系与空间结构，从而提升估计效率。通过模拟研究及实际调查数据的实证应用，验证了所提方法的实用性。