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CATEGORIES:Statistics
SUMMARY:Nonparametric estimation under shape constraints -
Piet Groeneboom\, Delft University
DTSTART;TZID=Europe/London:20131101T160000
DTEND;TZID=Europe/London:20131101T170000
UID:TALK47608AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/47608
DESCRIPTION:After pioneering work of (among others) Brunk\, Ch
ernoff and Prakasa Rao\, summarized in the book of
Barlow\, Bartholomew\, Bremner and Brunk\, the fi
eld of isotonic regression and shape constrained i
nference temporarily received less attention. But
there was a revival of interest in the nineties of
the preceding century because of several reasons.
\nFirst\, there was analytic progress when it beca
me clear how to compute the "Chernoffian distribut
ion"\, first studied by Chernoff in a study of an
estimator of the mode of a distribution. This aros
e from a study of the connection between Brownian
motion with a parabolic drift and Airy functions.
Second\, the relevance of the theory for nonparame
tric estimates of distribution functions in invers
e problems became apparent\, in particular for dec
onvolution and interval censoring models. And fina
lly\, fast algorithms became available for computi
ng the shape-constrained estimates. I will discuss
all three angles to these problems\, with an emph
asis on recent results and open problems.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:
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