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SUMMARY:From depth to local depth : a focus on centrality - Davy Paindavei
 ne\, Université libre de Bruxelles
DTSTART:20130503T150000Z
DTEND:20130503T160000Z
UID:TALK44868@talks.cam.ac.uk
CONTACT:Richard Samworth
DESCRIPTION:Aiming at analysing multimodal or non-convexly supported distr
 ibutions\nthrough data depth\, we introduce a local extension of depth. Ou
 r\nconstruction is obtained by conditioning the distribution to appropriat
 e\ndepth-based neighborhoods\, and has the advantages\, among others\, to 
 maintain\naffine-invariance and to apply to all depths in a generic way. M
 ost\nimportantly\, unlike their competitors\, that (for extreme localizati
 on)\nrather measure probability mass\, the resulting "local depths" focus 
 on\ncentrality and remain of a genuine depth nature at any locality level.
  We\nderive their main properties\, establish consistency of their sample\
 nversions\, and study their behavior under extreme localization. We presen
 t\ntwo applications of the proposed local depth (for classification and fo
 r\nsymmetry testing)\, and we extend our construction to the regression an
 d\nfunctional depth contexts. Throughout\, we illustrate the results on so
 me\,\nartificial and real\, univariate and multivariate data sets.\n\nThis
  is joint work with Germain van Bever.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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