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SUMMARY:Lecture 1 - Sample Covariance Operators: Normal Approximation and 
 Concentration - Professor Vladimir Koltchinskii\, Georgia Tech
DTSTART:20161109T140000Z
DTEND:20161109T160000Z
UID:TALK67784@talks.cam.ac.uk
CONTACT:CCA
DESCRIPTION:In this short course\, several problems related to statistical
  estimation of covariance operators and their spectral characteristics wil
 l be discussed. The problems will be studied in a dimension-free framework
  in which the data lives in high-dimensional or infinite-dimensional space
 s and "complexity" of estimation is characterized by the so called "effect
 ive rank" of the true covariance operator rather than by the dimension of 
 the ambient space. In this framework\, sharp moment bounds and concentrati
 on inequalities for the operator norm error of sample covariance will be p
 roved in the Gaussian case showing that the "effective rank" characterizes
  the size of this error.\n\nIn addition to this\, a number of recent resul
 ts on normal approximation and concentration of functions of sample covari
 ance operators\, including their spectral projections\, will be discussed.
LOCATION:MR15
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