Reconstruction of atomic measures from their halfspace depth

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10434778" target="_blank" >RIV/00216208:11320/21:10434778 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=WK3saMylph" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=WK3saMylph</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmva.2021.104727" target="_blank" >10.1016/j.jmva.2021.104727</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Reconstruction of atomic measures from their halfspace depth

Popis výsledku v původním jazyce

The halfspace depth can be seen as a mapping that to a finite Borel measure mu on the Euclidean space R-d assigns its depth, being a function R-d -&gt; [0, infinity): x -&gt; D (x; mu). The depth of mu quantifies how much centrally positioned a point x is with respect to mu. This function is intended to serve as generalization of the quantile function to multivariate spaces. We consider the problem of finding the inverse mapping to the halfspace depth: knowing only the function x -&gt; D (x; mu), our objective is to reconstruct the measure mu. We focus on mu atomic with finitely many atoms, and present a simple method for the reconstruction of the position and the weights of all atoms of mu, from its depth only. As a consequence, (i) we recover generalizations of several related results known from the literature, with substantially simplified proofs, and (ii) design a novel reconstruction procedure that is numerically more stable, and considerably faster than the known algorithms. Our analysis presents a comprehensive treatment of the halfspace depth of those measures whose depths attain finitely many different values. (C) 2021 Elsevier Inc. All rights reserved.

Název v anglickém jazyce

Reconstruction of atomic measures from their halfspace depth

Popis výsledku anglicky

The halfspace depth can be seen as a mapping that to a finite Borel measure mu on the Euclidean space R-d assigns its depth, being a function R-d -&gt; [0, infinity): x -&gt; D (x; mu). The depth of mu quantifies how much centrally positioned a point x is with respect to mu. This function is intended to serve as generalization of the quantile function to multivariate spaces. We consider the problem of finding the inverse mapping to the halfspace depth: knowing only the function x -&gt; D (x; mu), our objective is to reconstruct the measure mu. We focus on mu atomic with finitely many atoms, and present a simple method for the reconstruction of the position and the weights of all atoms of mu, from its depth only. As a consequence, (i) we recover generalizations of several related results known from the literature, with substantially simplified proofs, and (ii) design a novel reconstruction procedure that is numerically more stable, and considerably faster than the known algorithms. Our analysis presents a comprehensive treatment of the halfspace depth of those measures whose depths attain finitely many different values. (C) 2021 Elsevier Inc. All rights reserved.

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/GJ19-16097Y" target="_blank" >GJ19-16097Y: Geometrické aspekty matematické statistiky</a><br>

Návaznosti

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

Rok uplatnění

2021

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

183

Číslo periodika v rámci svazku

February

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

13

Strana od-do

104727

Kód UT WoS článku

000633380200003

EID výsledku v databázi Scopus

2-s2.0-85100400916