### Abstract

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 FOR. Storey introduced a point estimate of the FOR for fixed significance regions. The former approach conservatively controls the FOR at a fixed predetermined level, and the latter provides a conservatively biased estimate of the FOR 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 FOR controlling procedures. In the asymptotic setting, we also show that the point estimates can be used to estimate the FOR conservatively over all significance regions simultaneously, which is equivalent to controlling the FOR at all levels simultaneously. The main tool that we use is to translate existing FOR 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.

Original language | English (US) |
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Pages (from-to) | 187-205 |

Number of pages | 19 |

Journal | Journal of the Royal Statistical Society. Series B: Statistical Methodology |

Volume | 66 |

Issue number | 1 |

DOIs | |

State | Published - Feb 25 2004 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Keywords

- Multiple comparisons
- P-values
- Positive false discovery rate
- Q-values
- Simultaneous inference

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## Cite this

*Journal of the Royal Statistical Society. Series B: Statistical Methodology*,

*66*(1), 187-205. https://doi.org/10.1111/j.1467-9868.2004.00439.x