On Exact Computation of Tukey Depth Central Regions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10472949" target="_blank" >RIV/00216208:11320/24:10472949 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=US989TMV_2" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=US989TMV_2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/10618600.2023.2257781" target="_blank" >10.1080/10618600.2023.2257781</a>
Alternative languages
Result language
angličtina
Original language name
On Exact Computation of Tukey Depth Central Regions
Original language description
The Tukey (or halfspace) depth extends nonparametric methods toward multivariate data. The multivariate analogues of the quantiles are the central regions of the Tukey depth, defined as sets of points in the d-dimensional space whose Tukey depth exceeds given thresholds k. We address the problem of fast and exact computation of those central regions. First, we analyze an efficient Algorithm (A) from Liu, Mosler, and Mozharovskyi, and prove that it yields exact results in dimension d = 2, or for a low threshold k in arbitrary dimension. We provide examples where Algorithm (A) fails to recover the exact Tukey depth region for d > 2, and propose a modification that is guaranteed to be exact. We express the problem of computing the exact central region in its dual formulation, and use that viewpoint to demonstrate that further substantial improvements to our algorithm are unlikely. An efficient C++ implementation of our exact algorithm is freely available in the R package TukeyRegion.
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
—
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
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Computational and Graphical Statistics
ISSN
1061-8600
e-ISSN
1537-2715
Volume of the periodical
33
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
15
Pages from-to
699-713
UT code for WoS article
001122849600001
EID of the result in the Scopus database
2-s2.0-85177442788