Theoretical properties of angular halfspace depth

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10506629" target="_blank" >RIV/00216208:11320/25:10506629 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=HHHXssWHmk" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=HHHXssWHmk</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3150/24-BEJ1756" target="_blank" >10.3150/24-BEJ1756</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Theoretical properties of angular halfspace depth

Popis výsledku v původním jazyce

The angular halfspace depth (ahD) is a natural modification of the celebrated halfspace (or Tukey) depth to the setup of directional data. It allows us to define elements of nonparametric inference, such as the median, the inter-quantile regions, or the rank statistics, for datasets supported on the unit sphere. Despite being introduced in 1987, ahD has never received ample recognition in the literature, mainly due to the lack of efficient algorithms for its computation. With the recent progress on the computational front, ahD exhibits the potential for developing viable nonparametric statistics techniques for directional datasets. In this paper, we thoroughly treat the theoretical properties of ahD. We show that similarly to the classical halfspace depth for multivariate data, also ahD satisfies many desirable properties of a statistical depth function. Further, we derive uniform continuity/consistency results for the associated set of directional medians, and the central regions of ahD, the latter representing a depth-based analogue of the quantiles for directional data.

Název v anglickém jazyce

Theoretical properties of angular halfspace depth

Popis výsledku anglicky

The angular halfspace depth (ahD) is a natural modification of the celebrated halfspace (or Tukey) depth to the setup of directional data. It allows us to define elements of nonparametric inference, such as the median, the inter-quantile regions, or the rank statistics, for datasets supported on the unit sphere. Despite being introduced in 1987, ahD has never received ample recognition in the literature, mainly due to the lack of efficient algorithms for its computation. With the recent progress on the computational front, ahD exhibits the potential for developing viable nonparametric statistics techniques for directional datasets. In this paper, we thoroughly treat the theoretical properties of ahD. We show that similarly to the classical halfspace depth for multivariate data, also ahD satisfies many desirable properties of a statistical depth function. Further, we derive uniform continuity/consistency results for the associated set of directional medians, and the central regions of ahD, the latter representing a depth-based analogue of the quantiles for directional data.

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

Bernoulli

ISSN

1350-7265

e-ISSN

1573-9759

Svazek periodika

31

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

25

Strana od-do

1007-1031

Kód UT WoS článku

001426603800006

EID výsledku v databázi Scopus

2-s2.0-85218730663