### Abstract

The positive false discovery rate (pFDR) is the average proportion of false rejections given that the overall number of rejections is greater than zero. Assuming that the proportion of true null hypotheses, proportion of false positives, and proportion of true positives all converge pointwise, the pFDR converges to a continuous limit uniformly over all significance levels. We are showing that the uniform convergence still holds given a weaker assumption that the proportion of true positives converges in L ^{1}.

Original language | English |
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Pages (from-to) | 4239-4246 |

Number of pages | 8 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 42 |

Issue number | 23 |

DOIs | |

Publication status | Published - Dec 2 2013 |

Externally published | Yes |

### Fingerprint

### Keywords

- Differentially expressed genes
- FDR
- Microarray data
- Multiple testing
- pFDR

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

*Communications in Statistics - Theory and Methods*,

*42*(23), 4239-4246. https://doi.org/10.1080/03610926.2011.648787

**A positive false discovery rate convergence result.** / Melnykov, Igor.

Research output: Contribution to journal › Article

*Communications in Statistics - Theory and Methods*, vol. 42, no. 23, pp. 4239-4246. https://doi.org/10.1080/03610926.2011.648787

}

TY - JOUR

T1 - A positive false discovery rate convergence result

AU - Melnykov, Igor

PY - 2013/12/2

Y1 - 2013/12/2

N2 - The positive false discovery rate (pFDR) is the average proportion of false rejections given that the overall number of rejections is greater than zero. Assuming that the proportion of true null hypotheses, proportion of false positives, and proportion of true positives all converge pointwise, the pFDR converges to a continuous limit uniformly over all significance levels. We are showing that the uniform convergence still holds given a weaker assumption that the proportion of true positives converges in L 1.

AB - The positive false discovery rate (pFDR) is the average proportion of false rejections given that the overall number of rejections is greater than zero. Assuming that the proportion of true null hypotheses, proportion of false positives, and proportion of true positives all converge pointwise, the pFDR converges to a continuous limit uniformly over all significance levels. We are showing that the uniform convergence still holds given a weaker assumption that the proportion of true positives converges in L 1.

KW - Differentially expressed genes

KW - FDR

KW - Microarray data

KW - Multiple testing

KW - pFDR

UR - http://www.scopus.com/inward/record.url?scp=84887441594&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887441594&partnerID=8YFLogxK

U2 - 10.1080/03610926.2011.648787

DO - 10.1080/03610926.2011.648787

M3 - Article

VL - 42

SP - 4239

EP - 4246

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 23

ER -