Small area estimation (SAE) is a common endeavor and is used in a variety of disciplines. In low- and middle-income countries (LMICs), in which household surveys provide the most reliable and timely source of data, SAE is vital for highlighting disparities in health and demographic indicators. Weighted estimators are ideal for inference, but for fine geographical partitions in which there are insufficient data, SAE models are required. The most common approach is Fay-Herriot area-level modeling in which the data requirements are a weighted estimate and an associated variance estimate. The latter can be undefined or unstable when data are sparse and so we propose a principled modification which is based on augmenting the available data with a prior sample from a hypothetical survey. This adjustment is generally available, respects the design and is simple to implement. We examine the empirical properties of the adjustment through simulation and illustrate its use with wasting data from a 2018 Zambian Demographic and Health Survey. The modification is implemented as an automatic remedy in the R package surveyPrev, which provides a comprehensive suite of tools for conducing SAE in LMICs.

翻译：小区域估计（SAE）是一项常见的研究工作，广泛应用于多个学科领域。在低收入和中等收入国家（LMICs）中，家庭调查提供了最可靠且及时的数据来源，SAE对于揭示健康和人口指标的不平等现象至关重要。加权估计量是进行统计推断的理想选择，但对于数据不足的精细地理分区，则需要采用SAE模型。最常用的方法是Fay-Herriot区域层次建模，其数据要求包括加权估计值及相应的方差估计值。当数据稀疏时，方差估计值可能无法定义或极不稳定，因此我们提出一种基于原则的改进方法：通过添加来自假设调查的先验样本对现有数据进行扩充。这种调整方法具有普适性，尊重调查设计且易于实施。我们通过模拟实验检验了该调整方法的经验性质，并以2018年赞比亚人口与健康调查中的消瘦数据为例进行了应用演示。该改进方法已在R软件包surveyPrev中实现为自动校正工具，该软件包为在LMICs开展SAE研究提供了一套完整的工具集。