Exact and approximate computation of the scatter 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%3A10507218" target="_blank" >RIV/00216208:11320/25:10507218 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=bLKXOYQudC" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=bLKXOYQudC</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00180-024-01500-6" target="_blank" >10.1007/s00180-024-01500-6</a>
Alternative languages
Result language
angličtina
Original language name
Exact and approximate computation of the scatter halfspace depth
Original language description
The scatter halfspace depth (sHD) is an extension of the location halfspace (also called Tukey) depth that is applicable in the nonparametric analysis of scatter. Using sHD, it is possible to define minimax optimal robust scatter estimators for multivariate data. The problem of exact computation of sHD for data of dimension d >= 2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$d ge 2$$end{document} has, however, not been addressed in the literature. We develop an exact algorithm for the computation of sHD in any dimension d and implement it efficiently for any dimension d >= 1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$d ge 1$$end{document}. Since the exact computation of sHD is slow especially for higher dimensions, we also propose two fast approximate algorithms. All our programs are freely available in the R package scatterdepth.
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
Computational Statistics
ISSN
0943-4062
e-ISSN
1613-9658
Volume of the periodical
40
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
26
Pages from-to
547-572
UT code for WoS article
001216043500001
EID of the result in the Scopus database
2-s2.0-85192778281