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SUMMARY:Extrema of high dimensional data
DTSTART;VALUE=DATE-TIME:20220804T120000Z
DTEND;VALUE=DATE-TIME:20220804T122000Z
DTSTAMP;VALUE=DATE-TIME:20231211T163239Z
UID:indico-contribution-1218@conference2.aau.at
DESCRIPTION:In this talk we present a method to determine the directions
of multivariate extremes. Therefore the concept of sparse regular variatio
n of Meyer and Wintenberger (2021b) is introduced. In contrast to regular
variation the limit measure in the definition of sparse regular variation
is more sparse. The limit measure is called spectral measure and models th
e dependence in extremes. Sparse regular variation is based on an Euclide
an projection onto the simplex and allows the categorization of extremes w
ith respect to the cones of the simplex. The support of the spectral measu
re is determined by finding components in the data which are very large\,
while all other components are small. This is done by categorization of ex
tremes to cones of the simplex and fitting a multinomial model to the numb
er of extremes in the different cones (Meyer and Wintenberger (2021a)). Fo
r estimating the number of extremal cones we derive some information crite
ria\, e.g. AIC (Meyer and Wintenberger (2021a)).\n\nReferences:\nMeyer\, N
. and O. Wintenberger (2021a). "Multivariate sparse clustering for extreme
s". In: arXiv: 2007.11848 [math.ST].\n\nMeyer\, N. and O. Wintenberger (20
21b). "Sparse regular variation". In: Advances in Applied Probability 53(4
)\, pp. 1115-1148.\n\nhttps://conference2.aau.at/event/131/contributions/1
218/
LOCATION:Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1218/
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