## The Annals of Statistics

### A stochastic process approach to false discovery control

#### 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.

#### Article information

Source
Ann. Statist. Volume 32, Number 3 (2004), 1035-1061.

Dates
First available in Project Euclid: 24 May 2004

http://projecteuclid.org/euclid.aos/1085408494

Digital Object Identifier
doi:10.1214/009053604000000283

Mathematical Reviews number (MathSciNet)
MR2065197

Zentralblatt MATH identifier
02100792

Subjects
Primary: 62H15: Hypothesis testing 62G10: Hypothesis testing

#### Citation

Genovese, Christopher; Wasserman, Larry. A stochastic process approach to false discovery control. Ann. Statist. 32 (2004), no. 3, 1035--1061. doi:10.1214/009053604000000283. http://projecteuclid.org/euclid.aos/1085408494.

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