Strong Control, Conservative Point Estimation and Simultaneous Conservative Consistency of False Discovery Rates: A Unified Approach
Top Cited Papers
- 22 December 2003
- journal article
- Published by Oxford University Press (OUP) in Journal of the Royal Statistical Society Series B: Statistical Methodology
- Vol. 66 (1), 187-205
- https://doi.org/10.1111/j.1467-9868.2004.00439.x
Abstract
Summary. The false discovery rate (FDR) is a multiple hypothesis testing quantity that describes the expected proportion of false positive results among all rejected null hypotheses. Benjamini and Hochberg introduced this quantity and proved that a particular step-up p-value method controls the FDR. Storey introduced a point estimate of the FDR for fixed significance regions. The former approach conservatively controls the FDR at a fixed predetermined level, and the latter provides a conservatively biased estimate of the FDR for a fixed predetermined significance region. In this work, we show in both finite sample and asymptotic settings that the goals of the two approaches are essentially equivalent. In particular, the FDR point estimates can be used to define valid FDR controlling procedures. In the asymptotic setting, we also show that the point estimates can be used to estimate the FDR conservatively over all significance regions simultaneously, which is equivalent to controlling the FDR at all levels simultaneously. The main tool that we use is to translate existing FDR methods into procedures involving empirical processes. This simplifies finite sample proofs, provides a framework for asymptotic results and proves that these procedures are valid even under certain forms of dependence.Keywords
This publication has 12 references indexed in Scilit:
- A Direct Approach to False Discovery RatesJournal of the Royal Statistical Society Series B: Statistical Methodology, 2002
- Operating Characteristics and Extensions of the False Discovery Rate ProcedureJournal of the Royal Statistical Society Series B: Statistical Methodology, 2002
- Multiple hypotheses testing and expected number of type I. errorsThe Annals of Statistics, 2002
- Empirical Bayes Analysis of a Microarray ExperimentJournal of the American Statistical Association, 2001
- On the False Discovery Rate and Expected Type I ErrorsBiometrical Journal, 2001
- The control of the false discovery rate in multiple testing under dependencyThe Annals of Statistics, 2001
- Resampling-based false discovery rate controlling multiple test procedures for correlated test statisticsJournal of Statistical Planning and Inference, 1999
- A step-down multiple hypotheses testing procedure that controls the false discovery rate under independenceJournal of Statistical Planning and Inference, 1999
- Multiple Hypothesis TestingAnnual Review of Psychology, 1995
- An improved Bonferroni procedure for multiple tests of significanceBiometrika, 1986