Explicit bivariate simplicial depth
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10490146" target="_blank" >RIV/00216208:11320/25:10490146 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=bQO9_9ogW9" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=bQO9_9ogW9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmva.2024.105375" target="_blank" >10.1016/j.jmva.2024.105375</a>
Alternative languages
Result language
angličtina
Original language name
Explicit bivariate simplicial depth
Original language description
The simplicial depth (SD) is a celebrated tool defining elements of nonparametric and robust statistics for multivariate data. While many properties of SD are well-established, and its applications are abundant, explicit expressions for SD are known only for a handful of the simplest multivariate probability distributions. This paper deals with SD in the plane. It (i) develops a one-dimensional integral formula for SD of any properly continuous probability distribution, (ii) gives exact explicit expressions for SD of uniform distributions on (both convex and non-convex) polygons in the plane or on the boundaries of such polygons, and (iii) discusses several implications of these findings to probability and statistics: (a) An upper bound on the maximum SD in the plane, (b) an implication for a test of symmetry of a bivariate distribution, and (c) a connection of SD with the classical Sylvester problem from geometric probability.
Czech name
—
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
<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
Journal of Multivariate Analysis
ISSN
0047-259X
e-ISSN
1095-7243
Volume of the periodical
205
Issue of the periodical within the volume
January 2025
Country of publishing house
US - UNITED STATES
Number of pages
19
Pages from-to
105375
UT code for WoS article
001330760500001
EID of the result in the Scopus database
2-s2.0-85205324308