Simple halfspace depth

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10452033" target="_blank" >RIV/00216208:11320/22:10452033 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=yhlP1xVJGy" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=yhlP1xVJGy</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1214/22-ECP503" target="_blank" >10.1214/22-ECP503</a>

Result language
angličtina
Original language name
Simple halfspace depth
Original language description
The halfspace depth is a prominent tool of nonparametric inference for multivariate data. We consider it in the general context of finite Borel measures µ on Rd. The halfspace depth of a point x ELEMENT OF Rd is defined as the infimum of the µ-masses of halfspaces that contain x. We say that a measure µ has a simple (halfspace) depth if the set of all attained halfspace depth values of µ on Rd is finite. We give a complete description of measures with simple depths by showing that the halfspace depth of µ is simple if and only if µ is atomic with finitely many atoms. This result completely resolves the halfspace depth characterization problem for the particular situation of simple halfspace depths and datasets. We also discuss the cardinality of the set of the attained halfspace depth values.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10103 - Statistics and probability

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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