Asymptotically optimal, sequential, multiple testing procedures with prior information on the number of signals

Y. Song, G. Fellouris

Research output: Contribution to journalArticle

Abstract

Assuming that data are collected sequentially from independent streams, we consider the simultaneous testing of multiple binary hypotheses under two general setups; when the number of signals (correct alternatives) is known in advance, and when we only have a lower and an upper bound for it. In each of these setups, we propose feasible procedures that control, without any distributional assumptions, the familywise error probabilities of both type I and type II below given, user-specified levels. Then, in the case of i.i.d. observations in each stream, we show that the proposed procedures achieve the optimal expected sample size, under every possible signal configuration, asymptotically as the two error probabilities vanish at arbitrary rates. A simulation study is presented in a completely symmetric case and supports insights obtained from our asymptotic results, such as the fact that knowledge of the exact number of signals roughly halves the expected number of observations compared to the case of no prior information.

Original languageEnglish (US)
Pages (from-to)338-363
Number of pages26
JournalElectronic Journal of Statistics
Volume11
Issue number1
DOIs
StatePublished - Jan 1 2017

Keywords

  • Asymptotic optimality
  • Multiple testing
  • Prior information
  • Sequential analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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