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SUMMARY:Lecture 2 - Sample Covariance Operators: Normal Approximation and 
 Concentration - Professor Vladimir Koltchinskii\, Georgia Tech
DTSTART:20161111T140000Z
DTEND:20161111T160000Z
UID:TALK67785@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 “
 effective rank” of the true covariance operator rather than by the dimen
 sion of the ambient space. In this framework\, sharp moment bounds and con
 centration inequalities for the operator norm error of sample covariance w
 ill be proved in the Gaussian case showing that the “effective rank” c
 haracterizes the size of this error.\n\nIn addition to this\, a number of 
 recent results on normal approximation and concentration of functions of s
 ample covariance operators\, including their spectral projections\, will b
 e discussed.
LOCATION:MR12
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