A note on adaptive Bonferroni and Holm procedures under dependence

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Hochberg & Benjamini (1990) first presented adaptive procedures for controlling familywise error rate. However, until now, it has not been proved that these procedures control the familywise error rate. We introduce a simplified version of Hochberg & Benjamini's adaptive Bonferroni and Holm procedures. Assuming a conditional dependence model, we prove that the former procedure controls the familywise error rate in finite samples while the latter controls it approximately.

Original languageEnglish (US)
Pages (from-to)1012-1018
Number of pages7
Issue number4
StatePublished - Dec 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • General Mathematics
  • Agricultural and Biological Sciences (miscellaneous)
  • General Agricultural and Biological Sciences
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


  • Bonferroni procedure
  • Conditional dependence
  • Familywise error rate
  • Holm procedure
  • Multiple testing
  • Step-down procedure


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