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CATEGORIES:Cambridge Centre for Analysis talks
SUMMARY:Lecture 1 - Sample Covariance Operators: Normal Ap
proximation and Concentration - Professor Vladimir
Koltchinskii\, Georgia Tech
DTSTART;TZID=Europe/London:20161109T140000
DTEND;TZID=Europe/London:20161109T160000
UID:TALK67784AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/67784
DESCRIPTION:In this short course\, several problems related to
statistical estimation of covariance operators an
d their spectral characteristics will be discussed
. The problems will be studied in a dimension-free
framework in which the data lives in high-dimensi
onal or infinite-dimensional spaces and "complexit
y" of estimation is characterized by the so called
"effective rank" of the true covariance operator
rather than by the dimension of the ambient space.
In this framework\, sharp moment bounds and conce
ntration inequalities for the operator norm error
of sample covariance will be proved in the Gaussia
n case showing that the "effective rank" character
izes the size of this error.\n\nIn addition to thi
s\, a number of recent results on normal approxima
tion and concentration of functions of sample cova
riance operators\, including their spectral projec
tions\, will be discussed.
LOCATION:MR15
CONTACT:CCA
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