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CATEGORIES:Statistics
SUMMARY:Short Course: Lecture 2 - Sample Covariance Operat
ors: Normal Approximation and Concentration - Prof
essor Vladimir Koltchinskii\, Georgia Tech.
DTSTART;TZID=Europe/London:20161111T140000
DTEND;TZID=Europe/London:20161111T160000
UID:TALK68860AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/68860
DESCRIPTION:Lecture 2 – \n\nIn this short course\, several pro
blems related to statistical estimation of covaria
nce operators\n\nand their spectral characteristic
s will be discussed. The problems will be studied
in a dimension-free framework in which the data li
ves in high-dimensional or infinite-dimensional sp
aces and ``complexity"\n\nof estimation is charact
erized by the so called ``effective rank'' of the
true covariance operator rather than by the dimens
ion of the ambient space. In this framework\, shar
p moment bounds and concentration inequalities for
the operator norm error of sample covariance will
be proved\n\nin the Gaussian case showing that th
e ``effective rank'' characterizes the size of thi
s error.\n\nIn addition to this\, a number of rece
nt results on normal approximation and concentrati
on of\n\nfunctions of sample covariance operators\
, including their spectral projections\, will be d
iscussed.\n\n\n
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge.
CONTACT:HoD Secretary\, DPMMS
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