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Selective inference on multiple families of hypotheses

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  • Yoav Benjamini
  • Marina Bogomolov

Abstract

type="main" xml:id="rssb12028-abs-0001"> In many complex multiple-testing problems the hypotheses are divided into families. Given the data, families with evidence for true discoveries are selected, and hypotheses within them are tested. Neither controlling the error rate in each family separately nor controlling the error rate over all hypotheses together can assure some level of confidence about the filtration of errors within the selected families. We formulate this concern about selective inference in its generality, for a very wide class of error rates and for any selection criterion, and present an adjustment of the testing level inside the selected families that retains control of the expected average error over the selected families.

Suggested Citation

  • Yoav Benjamini & Marina Bogomolov, 2014. "Selective inference on multiple families of hypotheses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 297-318, January.
    • Handle: RePEc:bla:jorssb:v:76:y:2014:i:1:p:297-318
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    File URL: http://hdl.handle.net/10.1111/rssb.2013.76.issue-1
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    Citations

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    Cited by:

    1. Hunt, Ian, 2022. "In-sample tests of predictability are superior to pseudo-out-of-sample tests, even when data mining," International Journal of Forecasting, Elsevier, vol. 38(3), pages 872-877.
    2. Guillermo Durand & Gilles Blanchard & Pierre Neuvial & Etienne Roquain, 2020. "Post hoc false positive control for structured hypotheses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1114-1148, December.
    3. Chang, Chiu-Lan & Cai, Qingyun, 2023. "Stock return anomalies identification during the Covid-19 with the application of a grouped multiple comparison procedure," Economic Analysis and Policy, Elsevier, vol. 79(C), pages 168-183.
    4. Vincent, Kendro & Hsu, Yu-Chin & Lin, Hsiou-Wei, 2021. "Investment styles and the multiple testing of cross-sectional stock return predictability," Journal of Financial Markets, Elsevier, vol. 56(C).
    5. Qingyun Cai & Hock Peng Chan, 2017. "A Double Application of the Benjamini-Hochberg Procedure for Testing Batched Hypotheses," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 429-443, June.
    6. Yu-Chin Hsu & Hsiou-Wei Lin & Kendro Vincent, 2017. "Do Cross-Sectional Stock Return Predictors Pass the Test without Data-Snooping Bias?," IEAS Working Paper : academic research 17-A003, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    7. Rina Foygel Barber & Aaditya Ramdas, 2017. "The p-filter: multilayer false discovery rate control for grouped hypotheses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1247-1268, September.

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