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CATEGORIES:Statistics
SUMMARY:Short Course: Lecture 1 - Sample Covariance Operat
ors: Normal Approximation and Concentration - Pro
fessor Vladimir Koltchinskii\, Georgia Tech.
DTSTART;TZID=Europe/London:20161109T140000
DTEND;TZID=Europe/London:20161109T160000
UID:TALK68859AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/68859
DESCRIPTION:Short Course Lecture 1 – \n\nIn this short course\
, several problems related to statistical estimati
on of covariance operators\n\nand their spectral c
haracteristics will be discussed. The problems wil
l be studied in a dimension-free framework in whic
h the data lives in high-dimensional or infinite-d
imensional spaces and ``complexity"\n\nof estimati
on is characterized by the so called ``effective r
ank'' of the true covariance operator rather than
by the dimension of the ambient space. In this fra
mework\, sharp moment bounds and concentration ine
qualities for the operator norm error of sample co
variance will be proved\n\nin the Gaussian case sh
owing that the ``effective rank'' characterizes th
e size of this error.\n\nIn addition to this\, a n
umber of recent results on normal approximation an
d concentration of\n\nfunctions of sample covarian
ce operators\, including their spectral projection
s\, will be discussed.\n\n\n
LOCATION:MR15\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge.
CONTACT:HoD Secretary\, DPMMS
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