Sequential multiple testing with generalized error control: An asymptotic optimality theory 1

Yanglei Song, Georgios Fellouris

Research output: Contribution to journalArticlepeer-review

Abstract

The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least k mistakes, of any kind, is controlled. Under the second, the probabilities of at least k 1 false positives and at least k 2 false negatives are simultaneously controlled. For each formulation, the optimal expected sample size is characterized, to a first-order asymptotic approximation as the error probabilities go to 0, and a novel multiple testing procedure is proposed and shown to be asymptotically efficient under every signal configuration. These results are established when the data streams for the various hypotheses are independent and each local log-likelihood ratio statistic satisfies a certain strong law of large numbers. In the special case of i.i.d. observations in each stream, the gains of the proposed sequential procedures over fixed-sample size schemes are quantified.

Original languageEnglish (US)
Pages (from-to)1776-1803
Number of pages28
JournalAnnals of Statistics
Volume47
Issue number3
DOIs
StatePublished - Jan 2019

Keywords

  • Asymptotic optimality
  • Generalized familywise error rates
  • Misclassification rate
  • Multiple testing
  • Sequential analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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