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SUMMARY:Short Course: Lecture 1 - Sample Covariance Operators: Normal Appr
 oximation and Concentration  - Professor Vladimir Koltchinskii\, Georgia T
 ech.
DTSTART:20161109T140000Z
DTEND:20161109T160000Z
UID:TALK68859@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:Short Course Lecture 1 – \n\nIn this short course\, several 
 problems related to statistical estimation of covariance operators\n\nand 
 their spectral characteristics will be discussed. The problems will be stu
 died in a dimension-free framework in which the data lives in high-dimensi
 onal or infinite-dimensional spaces and ``complexity"\n\nof estimation is 
 characterized by the so called ``effective rank'' of the true covariance o
 perator rather than by the dimension of the ambient space. In this framewo
 rk\, sharp moment bounds and concentration inequalities for the operator n
 orm error of sample covariance will be proved\n\nin the Gaussian case show
 ing that the ``effective rank'' characterizes the size of this error.\n\nI
 n addition to this\, a number of recent results on normal approximation an
 d concentration of\n\nfunctions of sample covariance operators\, including
  their spectral projections\, will be discussed.\n\n\n
LOCATION:MR15\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge.
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