Selective inference on multiple families of hypotheses

Yoav Benjamini, Marina Bogomolov

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)297-318
Number of pages22
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume76
Issue number1
DOIs
StatePublished - Jan 2014

Keywords

  • False discovery rate
  • Familywise error rate
  • Hierarchical testing
  • Multiple testing
  • Selective inference

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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