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SUMMARY:On adaptation of false discovery rate - Etienne Roquain\, Universi
 té Paris 6\, Pierre et Marie Curie
DTSTART:20111028T150000Z
DTEND:20111028T160000Z
UID:TALK32520@talks.cam.ac.uk
CONTACT:Richard Samworth
DESCRIPTION:The false discovery rate (FDR) is a tool coming from multiple 
 testing theory which is extensively used in many practical applications li
 ke microarrays\, neuroimaging and source detection. It is defined as the e
 xpected proportion of errors among the items declared as significant. Main
 taining this (expected) ratio below a nominal level α provides a global t
 ype I error control for which many items can be declared as significant\, 
 even if the dimension strongly increases.\n\nSurprisingly\, the FDR \, whi
 ch was initially designed to address a pure multiple testing problem\, has
  recently been shown to enjoy remarkable properties in other frameworks of
  statistical decision theory\, as estimation or classification. Namely\, w
 hen the signal is sparse\, it is adaptive to the unknown sparsity containe
 d in the data.\n\nIn this talk\, after a short presentation of the FDR con
 cept\, we will investigate the adaptation to the unknown sparsity of the F
 DR thresholding in a classification setting where the "0"-class (null) is 
 assumed to have a known\, symmetric log-concave density while the "1"-clas
 s (alternative) is obtained from the "0"-class either by translation (loca
 tion model) or by scaling (scale model). Non-asymptotic oracle inequalitie
 s are derived for the excess risk of FDR thresholding and an explicit choi
 ce for the nominal level α is proposed. Numerical experiments show that t
 he proposed choice of α is relevant for a practical use.\n\n\nThis is a j
 oint work with Pierre Neuvial.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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