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CATEGORIES:Statistics
SUMMARY:Approximation by Log-Concave Distributions -  Lutz
  Dumbgen (University of Bern)
DTSTART;TZID=Europe/London:20100526T160000
DTEND;TZID=Europe/London:20100526T170000
UID:TALK24457AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/24457
DESCRIPTION:Multivariate distributions with log-concave densit
 ies are an\ninteresting nonparametric model contai
 ning many standard parametric\nfamilies such as Ga
 ussian distributions. In the first part of the tal
 k\nit is shown that this nonparametric model behav
 es almost like a\nparametric model in a certain se
 nse. Moreover\, we discuss the\napproximation of a
 n arbitrary distribution P by a log-concave one wi
 th\nrespect to a Kullback-Leibler type distance. N
 ecessary and sufficient\nconditions for the existe
 nce of such an approximation are presented.\nFurth
 ermore\, this approximation depends continuously o
 n the\ndistribution P with respect to Wasserstein 
 distance which has direct\nimplications for nonpar
 ametric maximum likelihood estimation. In the\nsec
 ond part we present applications to quantile estim
 ation in non- and\nsemiparametric regression model
 s.\n...\nThis is based on joint work with Andre Hu
 esler\, Kaspar Rufibach\,\nRichard Samworth and Do
 minic Schuhmacher\n\n\nhttp://www.stat.unibe.ch/co
 ntent/staff/personalhomepages/duembgen/index_eng.h
 tml/\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
 B
CONTACT:
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