Modeling Random Effects Using Global–Local Shrinkage Priors in Small Area Estimation

Small area estimation is becoming increasingly popular for survey statisticians. One very important program is Small Area Income and Poverty Estimation undertaken by the United States Bureau of the Census, which aims at providing estimates related to income and poverty based on American Community Survey data at the state level and even at lower levels of geography. This article introduces global–local (GL) shrinkage priors for random effects in small area estimation to capture wide area level variation when the number of small areas is very large. These priors employ two levels of parameters, global and local parameters, to express variances of area-specific random effects so that both small and large random effects can be captured properly. We show via simulations and data analysis that use of the GL priors can improve estimation results in most cases. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

小域估计（Small Area Estimation）在调查统计学家群体中正日益受到重视。美国人口普查局（United States Bureau of the Census）开展的小域收入与贫困估计（Small Area Income and Poverty Estimation）项目便是极具代表性的一项，该项目旨在基于美国社区调查（American Community Survey）数据，提供州级乃至更低地理层级的收入与贫困相关估计值。本文针对小域估计中的随机效应，提出全局-局部（GL）收缩先验，以在小域数量极多的场景下精准捕捉宽泛的区域层级变异。这类先验通过全局与局部两级参数刻画区域专属随机效应的方差，从而能够合理适配各类规模的随机效应。本文通过模拟实验与实证数据分析证实，在多数场景下应用该GL先验均可优化估计结果。本文的补充材料（含可复现本研究所需材料的标准化说明）可通过在线附录获取。