CIRM - Videos & books Library - Optimal and maximin procedures for multiple testing problems

Virtualconference

Auteurs : Rosset, Saharon (Auteur de la conférence)
CIRM (Editeur )

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Résumé : 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.

Mots-Clés : Multiple comparisons; hypothesis testing; false discovery rate

Codes MSC :
62F03 - Hypothesis testing
62J15 - Paired and multiple comparisons
62P10 - Applications of statistics to biology and medical sciences

Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2146/Slides/Rosset.pdf

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Hennenfent, Guillaume

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https://videos.cirm-math.fr/2020-06-05_Rosset.mp4

Informations sur la Rencontre

Nom de la Rencontre : Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2
Organisateurs de la Rencontre : Bogdan, Malgorzata ; Graczyk, Piotr ; Panloup, Fabien ; Proïa, Frédéric ; Roquain, Etienne
Dates : 15/06/2020 - 19/06/2020
Année de la rencontre : 2020
URL de la Rencontre : https://www.cirm-math.com/cirm-virtual-...

Données de citation

DOI : 10.24350/CIRM.V.19642803
Citer cette vidéo: Rosset, Saharon (2020). Optimal and maximin procedures for multiple testing problems. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19642803
URI : http://dx.doi.org/10.24350/CIRM.V.19642803

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Bibliographie

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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