Explicit bivariate simplicial depth

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Explicit bivariate simplicial depth

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Explicit bivariate simplicial depth

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA24-10822S" target="_blank" >GA24-10822S: Geometrická vícerozměrná a ne-euklidovská statistika</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Multivariate Analysis

ISSN

0047-259X

e-ISSN

1095-7243

Svazek periodika

205

Číslo periodika v rámci svazku

January 2025

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

19

Strana od-do

105375

Kód UT WoS článku

001330760500001

EID výsledku v databázi Scopus

2-s2.0-85205324308