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

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  • Katarzyna Reluga
  • María-José Lombardía
  • Stefan Sperlich

Abstract

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.

Suggested Citation

  • Katarzyna Reluga & María-José Lombardía & Stefan Sperlich, 2023. "Simultaneous Inference for Empirical Best Predictors With a Poverty Study in Small Areas," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(541), pages 583-595, January.
    • Handle: RePEc:taf:jnlasa:v:118:y:2023:i:541:p:583-595
    DOI: 10.1080/01621459.2021.1942014
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    Cited by:

    1. Christophe Quentin Valvason & Stefan Sperlich, 2024. "A Note on Simultaneous Confidence Intervals for Direct, Indirect and Synthetic Estimators," Stats, MDPI, vol. 7(1), pages 1-17, March.

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