Theoretical properties of angular halfspace depth
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10506629" target="_blank" >RIV/00216208:11320/25:10506629 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=HHHXssWHmk" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=HHHXssWHmk</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3150/24-BEJ1756" target="_blank" >10.3150/24-BEJ1756</a>
Alternative languages
Result language
angličtina
Original language name
Theoretical properties of angular halfspace depth
Original language description
The angular halfspace depth (ahD) is a natural modification of the celebrated halfspace (or Tukey) depth to the setup of directional data. It allows us to define elements of nonparametric inference, such as the median, the inter-quantile regions, or the rank statistics, for datasets supported on the unit sphere. Despite being introduced in 1987, ahD has never received ample recognition in the literature, mainly due to the lack of efficient algorithms for its computation. With the recent progress on the computational front, ahD exhibits the potential for developing viable nonparametric statistics techniques for directional datasets. In this paper, we thoroughly treat the theoretical properties of ahD. We show that similarly to the classical halfspace depth for multivariate data, also ahD satisfies many desirable properties of a statistical depth function. Further, we derive uniform continuity/consistency results for the associated set of directional medians, and the central regions of ahD, the latter representing a depth-based analogue of the quantiles for directional data.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10103 - Statistics and probability
Result continuities
Project
<a href="/en/project/GA24-10822S" target="_blank" >GA24-10822S: Geometric Multivariate and Non-Euclidean Statistics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Bernoulli
ISSN
1350-7265
e-ISSN
1573-9759
Volume of the periodical
31
Issue of the periodical within the volume
2
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
25
Pages from-to
1007-1031
UT code for WoS article
001426603800006
EID of the result in the Scopus database
2-s2.0-85218730663