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SUMMARY:Halfspace depth: Geometry of multivariate quantiles
DTSTART:20221028T151500
DTEND:20221028T170000
DTSTAMP:20260407T215704Z
UID:19a75b892b9f70be80d9d52e23bbf5375f0aac19c9e5e6538b7799af
CATEGORIES:Conferences - Seminars
DESCRIPTION:Stanislav Nagy (Charles University)\nStatistical depth is a no
 n-parametric tool applicable to multivariate and non-Euclidean data\, whos
 e goal is a reasonable generalisation of quantiles to multivariate and mor
 e exotic datasets. We discuss the halfspace depth\, arguably the most cruc
 ial depth in statistics. J. W. Tukey proposed that depth in 1975\; its rig
 orous investigation started in the 1990s\, and still\, an abundance of ope
 n problems stimulates research in the area.\n\nWe present surprising links
  of the halfspace depth with well-studied concepts from convex geometry. U
 sing these relations\, we partially resolve several open problems concerni
 ng depth. In particular\, we resolve the 30-year-old characterisation conj
 ecture\, asking whether two different measures can correspond to the same 
 halfspace depth.
LOCATION:MA A1 12 https://plan.epfl.ch/?room==MA%20A1%2012
STATUS:CONFIRMED
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