k-hull depth: in between simplicial and 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%3A10506632" target="_blank" >RIV/00216208:11320/25:10506632 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=TwI1tVxtuM" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=TwI1tVxtuM</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00362-025-01709-7" target="_blank" >10.1007/s00362-025-01709-7</a>
Alternative languages
Result language
angličtina
Original language name
k-hull depth: in between simplicial and halfspace depth
Original language description
This paper introduces the k-hull depth, a generalized version of the celebrated (Liu) simplicial depth for multivariate data. The k-hull depth of a point x is an element of Rddocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$varvec{x}in mathbb R<^>d$$end{document} is defined as the probability that the convex hull of k independently sampled points from a given probability distribution covers xdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$varvec{x}$$end{document}. For varying values of k, one obtains a collection of k-hull depth functions with different properties. We consider both the computation and the theoretical properties of k-hull depths. We show that (i) the computation of the k-hull depth for any k in the plane can be performed with the same complexity as for the standard simplicial depth, (ii) in a certain sense, the k-hull depths can be seen as "intermediate" between the simplicial depth and the (Tukey) halfspace depth, (iii) the k-hull depths satisfy many plausible properties of the simplicial depth known from the literature, while (iv) the induced notion of a multivariate median based on the k-hull depth is for certain values of k more robust than the standard simplicial median. The practical relevance of considering k-hull depths is explored through simulations.
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
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
Statistical Papers
ISSN
0932-5026
e-ISSN
1613-9798
Volume of the periodical
66
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
25
Pages from-to
88
UT code for WoS article
001482788000002
EID of the result in the Scopus database
2-s2.0-105004353178