Balanced control of generalized error rates

  • Romano J
  • Wolf M
  • 17

    Readers

    Mendeley users who have this article in their library.
  • 15

    Citations

    Citations of this article.

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 step-down 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 consider the 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 is paid to the construction of methods which implicitly take into account the dependence structure of the individual test statistics in order to further increase the ability to detect false null hypotheses. A general resampling and subsampling approach is presentedwhich achieves these objectives, at least asymptotically.

Author-supplied keywords

  • Bootstrap
  • False discovery proportion
  • Generalized family-wise error rate
  • Multiple testing
  • Step-down procedure

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Authors

  • Joseph Romano

  • Michael Wolf

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free