A weighted localization of halfspace depth and its properties

Kód výsledku v IS VaVaI

RIV/00216208:11320/17:10366035 - isvavai.cz

Výsledek na webu

http://dx.doi.org/10.1016/j.jmva.2017.02.008

DOI - Digital Object Identifier

10.1016/j.jmva.2017.02.008

Jazyk výsledku

angličtina

Název v původním jazyce

A weighted localization of halfspace depth and its properties

Popis výsledku v původním jazyce

Statistical depth functions are well-known nonparametric tools for analysing multivariate data. Halfspace depth is most frequently used, and while it has many desirable properties, it is dependent on global characteristics of the underlying distribution. In some circumstances, however, it may be desirable to take into account more local and intrinsic characteristics of the data. To this end, we introduce weighted halfspace depths in which the indicator function of closed halfspace is replaced by a more general weight function. Our approach, which calls in part on functions associated with conic sections, encompasses as special cases the notions of sample halfspace depth and kernel density estimation. We give several illustrations and prove the strong uniform consistency of weighted halfspace depth incorporating mild conditions on the weight function.

Název v anglickém jazyce

A weighted localization of halfspace depth and its properties

Popis výsledku anglicky

Statistical depth functions are well-known nonparametric tools for analysing multivariate data. Halfspace depth is most frequently used, and while it has many desirable properties, it is dependent on global characteristics of the underlying distribution. In some circumstances, however, it may be desirable to take into account more local and intrinsic characteristics of the data. To this end, we introduce weighted halfspace depths in which the indicator function of closed halfspace is replaced by a more general weight function. Our approach, which calls in part on functions associated with conic sections, encompasses as special cases the notions of sample halfspace depth and kernel density estimation. We give several illustrations and prove the strong uniform consistency of weighted halfspace depth incorporating mild conditions on the weight function.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

GA14-07234S: Mnohorozměrné regresní kvantily v ekonometrii

Návaznosti

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

Rok uplatnění

2017

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

—

Svazek periodika

157

Číslo periodika v rámci svazku

157

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

17

Strana od-do

53-69

Kód UT WoS článku

000401299700005

EID výsledku v databázi Scopus

2-s2.0-85016462997