On a generalized false discovery rate

Sanat K. Sarkar, Wenge Guo

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


The concept of k-FWER has received much attention lately as an appropriate error rate for multiple testing when one seeks to control at least k false rejections, for some fixed k = ≥. A less conservative notion, the k-FDR, has been introduced very recently by Sarkar [Ann. Statist. 34 (2006) 394-415], generalizing the false discovery rate of Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289-300]. In this article, we bring newer insight to the k-FDR considering a mixture model involving independent p-values before motivating the developments of some new procedures that control it. We prove the k-FDR control of the proposed methods under a slightly weaker condition than in the mixture model. We provide numerical evidence of the proposed methods' superior power performance over some k-FWER and k- FDR methods. Finally, we apply our methods to a real data set.

Original languageEnglish (US)
Pages (from-to)1545-1565
Number of pages21
JournalAnnals of Statistics
Issue number3
StatePublished - Jun 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Average power
  • Gene expression
  • Generalized FDR
  • Generalized FWER
  • Multiple hypothesis testing
  • Oracle k-FDR procedure
  • Stepup procedures


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