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%3A10507222" target="_blank" >RIV/00216208:11320/25:10507222 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=GhdNtWbDm3" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=GhdNtWbDm3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/wics.70038" target="_blank" >10.1002/wics.70038</a>
Alternative languages
Result language
angličtina
Original language name
Halfspace Depth
Original language description
The halfspace depth (HD, also called Tukey depth) is a nonparametric tool of multivariate statistics that has found many applications in exploratory analysis, estimation, and statistical testing. For a dataset, it can be defined as the minimum portion of data points in the d$$ d $$-space that can be cut off by a hyperplane passing through a given point; in a probabilistic setting, it is defined as the smallest probability of a closed halfspace containing a given point. The HD can be seen as a generalization of quantiles to multivariate data based on a projection pursuit principle. It naturally induces a robust multivariate median, and the contours of the HD function give information about the geometry of the underlying dataset/probability distribution. We provide a high-level overview of the most important theoretical properties and applications of the HD for multivariate data. We also outline several extensions of the HD to additional settings, such as halfspace-like depths for directional, object, or functional data. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Statistical and Graphical Methods of Data Analysis > Robust Methods
Czech name
—
Czech description
—
Classification
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
Result continuities
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)
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
Wiley Interdisciplinary Reviews. Computational statistics
ISSN
1939-5108
e-ISSN
1939-0068
Volume of the periodical
17
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
18
Pages from-to
e70038
UT code for WoS article
001540706400001
EID of the result in the Scopus database
2-s2.0-105011691112