Partial reconstruction of measures from halfspace depth

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10452439" target="_blank" >RIV/00216208:11320/21:10452439 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/978-3-031-30164-3_8" target="_blank" >https://doi.org/10.1007/978-3-031-30164-3_8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-031-30164-3_8" target="_blank" >10.1007/978-3-031-30164-3_8</a>

Result language
angličtina
Original language name
Partial reconstruction of measures from halfspace depth
Original language description
The halfspace depth of a d-dimensional point x with respect to a finite (or probability) Borel measure μ in Rd is defined as the infimum of the μ-masses of all closed halfspaces containing x. A natural question is whether the halfspace depth, as a function of xELEMENT OFRd, determines the measure μ completely. In general, it turns out that this is not the case, and it is possible for two different measures to have the same halfspace depth function everywhere in Rd. In this paper we show that despite this negative result, one can still obtain a substantial amount of information on the support and the location of the mass of μ from its halfspace depth. We illustrate our partial reconstruction procedure in an example of a non-trivial bivariate probability distribution whose atomic part is determined successfully from its halfspace depth.
Czech name
—
Czech description
—

Project
<a href="/en/project/GX19-28231X" target="_blank" >GX19-28231X: DyMoDiF - Dynamic Models for the Digital Finance</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)