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Optimal and maximin procedures for multiple testing problems
Virtualconference
Authors : Rosset, Saharon (Author of the conference)
CIRM (Publisher )
62F03 - Hypothesis testing
62J15 - Paired and multiple comparisons
62P10 - Applications of statistics to biology and medical sciences
Additional resources :
https://www.cirm-math.fr/RepOrga/2146/Slides/Rosset.pdf
CIRM (Publisher )
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Abstract :
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.
Keywords : Multiple comparisons; hypothesis testing; false discovery rate
MSC Codes : Keywords : Multiple comparisons; hypothesis testing; false discovery rate
62F03 - Hypothesis testing
62J15 - Paired and multiple comparisons
62P10 - Applications of statistics to biology and medical sciences
Additional resources :
https://www.cirm-math.fr/RepOrga/2146/Slides/Rosset.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 15/06/2020 Conference Date : 05/06/2020 Subseries : Research talks arXiv category : Machine Learning ; Statistics Theory Mathematical Area(s) : Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:46:04 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2020-06-05_Rosset.mp4 
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Information on the Event
Event Title : Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2Event Organizers : Bogdan, Malgorzata ; Graczyk, Piotr ; Panloup, Fabien ; Proïa, Frédéric ; Roquain, Etienne Dates : 15/06/2020 - 19/06/2020 Event Year : 2020 Event URL : https://www.cirm-math.com/cirm-virtual-...
Citation Data
DOI : 10.24350/CIRM.V.19642803Cite this video as: 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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Bibliography
- 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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