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DTSTART:20170326T030000
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DTSTAMP:20260428T035849Z
UID:58cbbde621892802153783@ist.ac.at
DTSTART:20170330T164500
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DESCRIPTION:Speaker: Alexey Naumov\nhosted by Laszlo Erdös\nAbstract: Let 
 X_1\, ... \,X_n be i.i.d. sample in R^p with zero mean and covariance matr
 ix S. The problem of recovering the projector onto the eigenspace of S fro
 m these observations naturally arises in many applications. Recent techniq
 ue from [Koltchinskii and Lounici\, 2015] helps to study the asymptotic di
 stribution of the distance in the Frobenius norm between the true projecto
 r P_r on the subspace of the r-th eigenvalue and its empirical counterpart
  \\hat{P}_r in terms of the effective trace of S. This paper offers a boot
 strap procedure for building sharp confidence sets for the true projector 
 P_r from the given data. This procedure does not rely on the asymptotic di
 stribution of || P_r - \\hat{P}_r ||_2 and its moments\, it applies for sm
 all or moderate sample size n and large dimension p. The main result state
 s the validity of the proposed procedure for finite samples with an explic
 it error bound on the error of bootstrap approximation. This bound involve
 s some new sharp results on Gaussian comparison and Gaussian anti-concentr
 ation in high dimension. These are the joint results with V. Spokoiny and 
 V. Ulyanov.\n
LOCATION:Seminar room Big Ground floor / Office Bldg West (I21.EG.101)\, IS
 TA
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Alexey Naumov: Estimation of a spectral projector
URL:https://talks-calendar.ista.ac.at/events/384
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