Approximate computation of projection depths

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10434777" target="_blank" >RIV/00216208:11320/21:10434777 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=G_U9W1Dx3Y" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=G_U9W1Dx3Y</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.csda.2020.107166" target="_blank" >10.1016/j.csda.2020.107166</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Approximate computation of projection depths

Popis výsledku v původním jazyce

Data depth is a concept in multivariate statistics that measures the centrality of a point in a given data cloud in R-d. If the depth of a point can be represented as the minimum of the depths with respect to all one-dimensional projections of the data, then the depth satisfies the so-called projection property. Such depths form an important class that includes many of the depths that have been proposed in literature. For depths that satisfy the projection property an approximate algorithm can easily be constructed since taking the minimum of the depths with respect to only a finite number of one-dimensional projections yields an upper bound for the depth with respect to the multivariate data. Such an algorithm is particularly useful if no exact algorithm exists or if the exact algorithm has a high computational complexity, as is the case with the halfspace depth or the projection depth. To compute these depths in high dimensions, the use of an approximate algorithm with better complexity is surely preferable. Instead of focusing on a single method we provide a comprehensive and fair comparison of several methods, both already described in the literature and original. (C) 2021 Elsevier B.V. All rights reserved.

Název v anglickém jazyce

Approximate computation of projection depths

Popis výsledku anglicky

Data depth is a concept in multivariate statistics that measures the centrality of a point in a given data cloud in R-d. If the depth of a point can be represented as the minimum of the depths with respect to all one-dimensional projections of the data, then the depth satisfies the so-called projection property. Such depths form an important class that includes many of the depths that have been proposed in literature. For depths that satisfy the projection property an approximate algorithm can easily be constructed since taking the minimum of the depths with respect to only a finite number of one-dimensional projections yields an upper bound for the depth with respect to the multivariate data. Such an algorithm is particularly useful if no exact algorithm exists or if the exact algorithm has a high computational complexity, as is the case with the halfspace depth or the projection depth. To compute these depths in high dimensions, the use of an approximate algorithm with better complexity is surely preferable. Instead of focusing on a single method we provide a comprehensive and fair comparison of several methods, both already described in the literature and original. (C) 2021 Elsevier B.V. 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

Computational Statistics and Data Analysis

ISSN

0167-9473

e-ISSN

—

Svazek periodika

157

Číslo periodika v rámci svazku

January

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

23

Strana od-do

107166

Kód UT WoS článku

000620292000003

EID výsledku v databázi Scopus

2-s2.0-85099698819