Halfspace Depth
Identifikátory výsledku
Kód výsledku v 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>
Výsledek na webu
<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>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Halfspace Depth
Popis výsledku v původním jazyce
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
Název v anglickém jazyce
Halfspace Depth
Popis výsledku anglicky
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
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10103 - Statistics and probability
Návaznosti výsledku
Projekt
Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Ostatní
Rok uplatnění
2025
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Wiley Interdisciplinary Reviews. Computational statistics
ISSN
1939-5108
e-ISSN
1939-0068
Svazek periodika
17
Číslo periodika v rámci svazku
3
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
18
Strana od-do
e70038
Kód UT WoS článku
001540706400001
EID výsledku v databázi Scopus
2-s2.0-105011691112