A new multiple testing method in the dependent case1

Arthur Cohen, Harold B. Sackrowitz, Minya Xu

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

The most popular multiple testing procedures are stepwise procedures based on P-values for individual test statistics. Included among these are the false discovery rate (FDR) controlling procedures of Benjamini-Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289-300] and their offsprings. Even for models that entail dependent data, P-values based on marginal distributions are used. Unlike such methods, the new method takes dependency into account at all stages. Furthermore, the P-value procedures often lack an intuitive convexity property, which is needed for admissibility. Still further, the new methodology is computationally feasible. If the number of tests is large and the proportion of true alternatives is less than say 25 percent, simulations demonstrate a clear preference for the new methodology. Applications are detailed for models such as testing treatments against control (or any intraclass correlation model), testing for change points and testing means when correlation is successive.

Original languageEnglish (US)
Pages (from-to)1518-1544
Number of pages27
JournalAnnals of Statistics
Volume37
Issue number3
DOIs
StatePublished - Jun 1 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Admissibility
  • Change point problem
  • False discovery rate
  • Likelihood ratio
  • Residuals
  • Step-down procedure
  • Step-up procedure
  • Successive correlation model
  • Treatments vs. control
  • Two-sided alternatives
  • Vector risk

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