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SUMMARY:Approximation by Log-Concave Distributions -  Lutz Dumbgen (Univer
 sity of Bern)
DTSTART:20100526T150000Z
DTEND:20100526T160000Z
UID:TALK24457@talks.cam.ac.uk
CONTACT:8047
DESCRIPTION:Multivariate distributions with log-concave densities are an\n
 interesting nonparametric model containing many standard parametric\nfamil
 ies such as Gaussian distributions. In the first part of the talk\nit is s
 hown that this nonparametric model behaves almost like a\nparametric model
  in a certain sense. Moreover\, we discuss the\napproximation of an arbitr
 ary distribution P by a log-concave one with\nrespect to a Kullback-Leible
 r type distance. Necessary and sufficient\nconditions for the existence of
  such an approximation are presented.\nFurthermore\, this approximation de
 pends continuously on the\ndistribution P with respect to Wasserstein dist
 ance which has direct\nimplications for nonparametric maximum likelihood e
 stimation. In the\nsecond part we present applications to quantile estimat
 ion in non- and\nsemiparametric regression models.\n...\nThis is based on 
 joint work with Andre Huesler\, Kaspar Rufibach\,\nRichard Samworth and Do
 minic Schuhmacher\n\n\nhttp://www.stat.unibe.ch/content/staff/personalhome
 pages/duembgen/index_eng.html/\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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