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DTSTART:20170326T030000
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DTSTART:20161030T020000
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DTSTAMP:20260428T111748Z
UID:57f7915881f68780214077@ist.ac.at
DTSTART:20170307T160000
DTEND:20170307T180000
DESCRIPTION:Speaker: Johannes Heiny\nhosted by Laszlo Erdös\nAbstract: We 
 study the joint distributional convergence of the largest eigenvalues of t
 he sample covariance matrix of a p-dimensional heavy-tailed time series wh
 en p converges to infinity together with the sample size n. We generalize 
 the growth rates of p existing in the literature. Assuming a regular varia
 tion condition with tail index alpha<4\, we employ a large deviations appr
 oach to show that the extreme eigenvalues are essentially determined by th
 e extreme order statistics from an array of iid random variables. The asym
 ptotic behavior of the extreme eigenvalues is then derived routinely from 
 classical extreme value theory. The resulting approximations are strikingl
 y simple considering the high dimension of the problem at hand.\n\nWe deve
 lop a theory for the point process of the normalized eigenvalues of the sa
 mple covariance matrix in the case where rows and columns of the data are 
 linearly dependent. Based on the weak convergence of this point process we
  derive the limit laws of various functionals of the eigenvalues.\n\nThis 
 talk is based on a joint work with Richard Davis and Thomas Mikosch.\n
LOCATION:Seminar room Big Ground floor / Office Bldg West (I21.EG.101)\, IS
 TA
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Johannes Heiny: Limit theorems for the largest eigenvalues of the s
 ample covariance matrix of a heavy-tailed time series
URL:https://talks-calendar.ista.ac.at/events/298
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