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A Note on Simultaneous Confidence Intervals for Direct, Indirect and Synthetic Estimators

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  • Christophe Quentin Valvason

    (Geneva School of Economics and Management, University of Geneva, 40 Boulevard du Pont d’Arve, 1204 Geneva, Switzerland)

  • Stefan Sperlich

    (Geneva School of Economics and Management, University of Geneva, 40 Boulevard du Pont d’Arve, 1204 Geneva, Switzerland)

Abstract

Direct, indirect and synthetic estimators have a long history in official statistics. While model-based or model-assisted approaches have become very popular, direct and indirect estimators remain the predominant standard and are therefore important tools in practice. This is mainly due to their simplicity, including low data requirements, assumptions and straightforward inference. With the increasing use of domain estimates in policy, the demands on these tools have also increased. Today, they are frequently used for comparative statistics. This requires appropriate tools for simultaneous inference. We study devices for constructing simultaneous confidence intervals and show that simple tools like the Bonferroni correction can easily fail. In contrast, uniform inference based on max-type statistics in combination with bootstrap methods, appropriate for finite populations, work reasonably well. We illustrate our methods with frequently applied estimators of totals and means.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jstats:v:7:y:2024:i:1:p:20-349:d:1360387
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    References listed on IDEAS

    as
    1. Peter Kramlinger & Tatyana Krivobokova & Stefan Sperlich, 2023. "Marginal and Conditional Multiple Inference for Linear Mixed Model Predictors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(544), pages 2344-2355, October.
    2. Nikos Tzavidis & Li‐Chun Zhang & Angela Luna & Timo Schmid & Natalia Rojas‐Perilla, 2018. "From start to finish: a framework for the production of small area official statistics," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 927-979, October.
    3. Little R.J., 2004. "To Model or Not To Model? Competing Modes of Inference for Finite Population Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 546-556, January.
    4. Joseph P. Romano & Michael Wolf, 2005. "Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 94-108, March.
    5. 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.
    6. Katarzyna Reluga & María‐José Lombardía & Stefan Sperlich, 2023. "Simultaneous inference for linear mixed model parameters with an application to small area estimation," International Statistical Review, International Statistical Institute, vol. 91(2), pages 193-217, August.
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