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SUMMARY:Short Course: Lecture 2 - Sample Covariance Operators: Normal Appr
 oximation and Concentration - Professor Vladimir Koltchinskii\, Georgia Te
 ch.
DTSTART:20161111T140000Z
DTEND:20161111T160000Z
UID:TALK68860@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:Lecture 2 – \n\nIn this short course\, several problems rela
 ted to statistical estimation of covariance operators\n\nand their spectra
 l characteristics will be discussed. The problems will be studied in a dim
 ension-free framework in which the data lives in high-dimensional or infin
 ite-dimensional spaces and ``complexity"\n\nof estimation is characterized
  by the so called ``effective rank'' of the true covariance operator rathe
 r than by the dimension of the ambient space. In this framework\, sharp mo
 ment bounds and concentration inequalities for the operator norm error of 
 sample covariance will be proved\n\nin the Gaussian case showing that the 
 ``effective rank'' characterizes the size of this error.\n\nIn addition to
  this\, a number of recent results on normal approximation and concentrati
 on of\n\nfunctions of sample covariance operators\, including their spectr
 al projections\, will be discussed.\n\n\n
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge.
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