Simultaneous Inference for Empirical Best Predictors With a Poverty Study in Small Areas

• 成果类型: Article
• 署名作者: Reluga, Katarzyna; Lombardia, Maria-Jose; Sperlich, Stefan
• 署名单位: University of Cambridge; Universidade da Coruna; University of Geneva
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.1942014
• 发表日期: 2023
• 页码: 583-595
• 关键词: linear mixed models; likelihood inference; bootstrap; estimators; intervals

摘要

Today, generalized linear mixed models (GLMM) are broadly used in many fields. However, the development of tools for performing simultaneous inference has been largely neglected in this domain. A framework for joint inference is indispensable to carry out statistically valid multiple comparisons of parameters of interest between all or several clusters. We therefore develop simultaneous confidence intervals and multiple testing procedures for empirical best predictors under GLMM. In addition, we implement our methodology to study widely employed examples of mixed models, that is, the unit-level binomial, the area-level Poisson-gamma and the area-level Poisson-lognormal mixed models. The asymptotic results are accompanied by extensive simulations. A case study on predicting poverty rates illustrates applicability and advantages of our simultaneous inference tools.