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CATEGORIES:Probability
SUMMARY:Talagrand's concentration inequality for empirical
processes - Richard Nickl (Cambridge)
DTSTART;TZID=Europe/London:20081202T140000
DTEND;TZID=Europe/London:20081202T150000
UID:TALK14301AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/14301
DESCRIPTION:This is an expository talk about a deep probabilit
y inequality due to Talagrand (Invent. Math. 1996\
, cf. Ledoux's book in 2001)\, which gives a Proho
rov- (and then also Bernstein-) type exponential b
ound for the concentration of the supremum of an e
mpirical process around its mean. I will try to di
scuss the following points: A) Some ideas of the p
roof\, in particular the proof due to Ledoux using
logarithmic Sobolev inequalities\, which is relat
ed to the more general "concentration of measure"
phenomenon. B) Discuss a variety of probabilistic
applications\, which should show how versatile thi
s inequality is\, in particular that it reproduces
most known exp. inequalities for i.i.d. sums of (
possibly Banach-)valued random variables. C) Discu
ss recent statistical applications to adaptive est
imation\, model selection problems\, Rademacher pr
ocesses\, and almost sure limit laws (LIL-type res
ults).
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Berestycki
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