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Multidimensional symbolic dynamics and lattice models of quasicrystals / Dynamique symbolique multidimensionnelle et modèles de quasi-cristaux sur réseau
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Multidimensional symbolic dynamics and lattice models of quasicrystals / Dynamique symbolique multidimensionnelle et modèles de quasi-cristaux sur réseau

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Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2

Collection Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2

Organizer(s) Bogdan, Malgorzata ; Graczyk, Piotr ; Panloup, Fabien ; Proïa, Frédéric ; Roquain, Etienne
Date(s) 15/06/2020 - 19/06/2020
linked URL https://www.cirm-math.com/cirm-virtual-event-2146.html
00:00:00 / 00:00:00
21 25

Optimal and maximin procedures for multiple testing problems

By Saharon Rosset

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.

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Citation data

  • DOI 10.24350/CIRM.V.19642803
  • Cite this video Rosset, Saharon (05/06/2020). 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

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  • 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

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