00:00:00 / 00:00:00

Optimal and maximin procedures for multiple testing problems

By Saharon Rosset

Appears in collection : Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2

Multiple testing problems are a staple of modern statistics. The fundamental objective is to reject as many false null hypotheses as possible, subject to controlling an overall measure of false discovery, like family-wise error rate (FWER) or false discovery rate (FDR). We formulate multiple testing of simple hypotheses as an infinite-dimensional optimization problem, seeking the most powerful rejection policy which guarantees strong control of the selected measure. We show that for exchangeable hypotheses, for FWER or FDR and relevant notions of power, these problems lead to infinite programs that can provably be solved. We explore maximin rules for complex alternatives, and show they can be found in practice, leading to improved practical procedures compared to existing alternatives. We derive explicit optimal tests for FWER or FDR control for three independent normal means. We find that the power gain over natural competitors is substantial in all settings examined. We apply our optimal maximin rule to subgroup analyses in systematic reviews from the Cochrane library, leading to an increased number of findings compared to existing alternatives.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19642803
  • Cite this video Rosset Saharon (6/5/20). Optimal and maximin procedures for multiple testing problems. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19642803
  • URL https://dx.doi.org/10.24350/CIRM.V.19642803


  • ROSSET, Saharon, HELLER, Ruth, PAINSKY, Amichai, et al. Optimal and Maximin Procedures for Multiple Testing Problems. arXiv preprint arXiv:1804.10256, 2018. - https://arxiv.org/abs/1804.10256

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow


  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
  • Get notification updates
    for your favorite subjects
Give feedback