Simultaneous Inference for Empirical Best Predictors with a Poverty Study in Small Areas
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Today, generalized linear mixed models 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 for comparisons of clusters or small areas. Therefore we introduce simultaneous confidence intervals and develop multiple testing procedures for empirical best predictors. We consider area- and unit-level models to study poverty rates in the counties of Galicia in Spain. In this context we illustrate to what extent existing methods fail. Simulation studies and complete asymptotic theory are also provided.
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