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UID:20251121T151522EST-5818V6AIeH@132.216.98.100
DTSTAMP:20251121T201522Z
DESCRIPTION:Multivariate Geometric Expectiles.\n\nIn this talk we introduce
  a generalization of expectiles for d-dimensional multivariate distributio
 n functions. This generalization is based on geometric quantiles introduce
 d in Chaudhuri (1996). The resulting geometric expectiles are unique solut
 ions to a convex risk minimization problem and are given by $d$-dimensiona
 l vectors. We discuss their behaviour under common data transformations su
 ch as translations\, scaling and rotations of the underlying data. Geometr
 ic expectiles also obey symmetry properties comparable to the univariate c
 ase. We furthermore discuss elicitability in the context of geometric expe
 ctiles and multivariate risk measures in general. We show that a consisten
 t estimator is readily available by the sample version. Finally\, we exemp
 lify the usage of geometric expectiles as risk measures in a number of mul
 tivariate settings\, highlighting the influence of varying margins and dep
 endence structures. Joint work with Marius Hofert and Mélina Mailhot\n
DTSTART:20170420T193000Z
DTEND:20170420T203000Z
LOCATION:CA\, QC\, Sherbrooke\, Seminar Statistique Sherbrooke\, 2500 Boul 
 de L'Université
SUMMARY:Klaus Herrmann\, Department of Mathematics and Statistics\, Concord
 ia University
URL:/mathstat/channels/event/klaus-herrmann-department
 -mathematics-and-statistics-concordia-university-267648
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