"Consider the problem of testing s hypotheses simultaneously. In this paper, we derive methods which control the generalized familywise error rate given by the probability of k or more false rejections, abbreviated k-FWER. We derive both single-step and stepdown procedures that control the k-FWER in finite samples or asymptotically, depending on the situation. Moreover, the procedures are asymptotically balanced in an appropriate sense. We briefly consider control of the average number of false rejections. Additionally, we considernthe false discovery proportion (FDP), defined as the number of false rejections divided by the total number of rejections (and defined to be 0 if there are no rejections). Here, the goal is to construct methods which satisfy, for given γ and α, P{FDP > γ} ≤ α, at least asymptotically. Special attention attention is paid to the construction of methods which implicitly take into account the dependence structure of the individual test statistics in ordernto further increase the ability to detect false null hypotheses. A general resampling and subsampling approach is presented which achieves these objectives, at least asymptotically."

Romano, Joseph P; Wolf, Michael (2008). *Balanced Control of Generalized Error Rates.* Working paper series / Institute for Empirical Research in Economics No. 379, University of Zurich.

## Abstract

"Consider the problem of testing s hypotheses simultaneously. In this paper, we derive methods which control the generalized familywise error rate given by the probability of k or more false rejections, abbreviated k-FWER. We derive both single-step and stepdown procedures that control the k-FWER in finite samples or asymptotically, depending on the situation. Moreover, the procedures are asymptotically balanced in an appropriate sense. We briefly consider control of the average number of false rejections. Additionally, we considernthe false discovery proportion (FDP), defined as the number of false rejections divided by the total number of rejections (and defined to be 0 if there are no rejections). Here, the goal is to construct methods which satisfy, for given γ and α, P{FDP > γ} ≤ α, at least asymptotically. Special attention attention is paid to the construction of methods which implicitly take into account the dependence structure of the individual test statistics in ordernto further increase the ability to detect false null hypotheses. A general resampling and subsampling approach is presented which achieves these objectives, at least asymptotically."

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## Additional indexing

Item Type: | Working Paper |
---|---|

Communities & Collections: | 03 Faculty of Economics > Department of Economics
Working Paper Series > Institute for Empirical Research in Economics (former) |

Dewey Decimal Classification: | 330 Economics |

Language: | English |

Date: | July 2008 |

Deposited On: | 29 Nov 2011 22:47 |

Last Modified: | 05 Apr 2016 15:12 |

Series Name: | Working paper series / Institute for Empirical Research in Economics |

ISSN: | 1424-0459 |

Official URL: | http://www.econ.uzh.ch/wp.html |

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