A stochastic process approach to false discovery control

2004/05/27 by Christopher Genovese, Larry Wasserman · 9 citations
Decision Sciences · Mathematics · #Meta-analysis and systematic reviews #Statistical Methods and Bayesian Inference #Statistical Methods in Clinical Trials #math.ST #msc:62G10 #msc:62H15 #stat.TH

paper · pdf · doi:10.1214/009053604000000283

published as Annals of Statistics 2004, Vol. 32, No. 3, 1035-1061

openalex publication_date 2004/05/27 · arxiv created 2004/06/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

This paper extends the theory of false discovery rates (FDR) pioneered by Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289–300]. We develop a framework in which the False Discovery Proportion (FDP)—the number of false rejections divided by the number of rejections—is treated as a stochastic process. After obtaining the limiting distribution of the process, we demonstrate the validity of a class of procedures for controlling the False Discovery Rate (the expected FDP). We construct a confidence envelope for the whole FDP process. From these envelopes we derive confidence thresholds, for controlling the quantiles of the distribution of the FDP as well as controlling the number of false discoveries. We also investigate methods for estimating the p-value distribution.

Citations

• The control of the false discovery rate in multiple testing under dependency
• Adapting to unknown sparsity by controlling the false discovery rate
• Strong Control, Conservative Point Estimation and Simultaneous Conservative Consistency of False Discovery Rates: A Unified Approach

Cited by

• On false discovery control under dependence
• Properties of higher criticism under strong dependence
• Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses
• Comment: Microarrays, Empirical Bayes and the Two-Group Model
• Comment: Microarrays, Empirical Bayes and the Two-Groups Model
• Asymptotic properties of false discovery rate controlling procedures under independence
• Estimation and confidence sets for sparse normal mixtures
• The Benjamini--Hochberg Procedure Can Fail to Control the FDR for Correlated Two-Sided Gaussian Tests
• On the false discovery rate and an asymptotically optimal rejection curve