Title: On Methods Controlling the False Discovery Rate

Author(s): Sanat K. Sarkar
Issue: Volume 70 Series A Part 2 Year 2008
Pages: 135 -- 168
A great upsurge in research has taken place during the last decade or so in the area of multiple testing due to its increased relevance in modern scientific investigations. A major portion of this research has been devoted to developing methods that control error rates more meaningful as well as powerful than traditional ones in the context of these investigations. The error rates measuring false discovery proportion, particularly the false discovery rate (FDR), and procedures controlling them have received the most attention. This article relates specifically to the FDR and is written with two basic objectives: (i) To put together some important developments in theory and methodology of the FDR with finite number of hypotheses and report them with newer formulas, proofs and insights, and (ii) to develop an error rate extending the FDR to one that directly incorporates dependence among the test statistics and methods that control it.
AMS (2000) subject classification. Primary 62H35; Secondary 62G20, 62F40.
Keywords and phrases: Adpative BH methods, BH method, BY method, false non-discovery rate, pair-wise FDR, positive depende nce, multivariate totally positive of order two, stepwise multiple testing me thods.