Uniform convergence rates for the approximated halfspace and projection depth

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10418981" target="_blank" >RIV/00216208:11320/20:10418981 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=i9_ppNWMXR" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=i9_ppNWMXR</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1214/20-EJS1759" target="_blank" >10.1214/20-EJS1759</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Uniform convergence rates for the approximated halfspace and projection depth

Popis výsledku v původním jazyce

The computational complexity of some depths that satisfy the projection property, such as the halfspace depth or the projection depth, is known to be high, especially for data of higher dimensionality. In such scenarios, the exact depth is frequently approximated using a randomized approach: The data are projected into a finite number of directions uniformly distributed on the unit sphere, and the minimal depth of these univariate projections is used to approximate the true depth. We provide a theoretical background for this approximation procedure. Several uniform consistency results are established, and the corresponding uniform convergence rates are provided. For elliptically symmetric distributions and the halfspace depth it is shown that the obtained uniform convergence rates are sharp. In particular, guidelines for the choice of the number of random projections in order to achieve a given precision of the depths are stated.

Název v anglickém jazyce

Uniform convergence rates for the approximated halfspace and projection depth

Popis výsledku anglicky

The computational complexity of some depths that satisfy the projection property, such as the halfspace depth or the projection depth, is known to be high, especially for data of higher dimensionality. In such scenarios, the exact depth is frequently approximated using a randomized approach: The data are projected into a finite number of directions uniformly distributed on the unit sphere, and the minimal depth of these univariate projections is used to approximate the true depth. We provide a theoretical background for this approximation procedure. Several uniform consistency results are established, and the corresponding uniform convergence rates are provided. For elliptically symmetric distributions and the halfspace depth it is shown that the obtained uniform convergence rates are sharp. In particular, guidelines for the choice of the number of random projections in order to achieve a given precision of the depths are stated.

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

2020

Kód důvěrnosti údajů

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

Název periodika

Electronic Journal of Statistics

ISSN

1935-7524

e-ISSN

—

Svazek periodika

14

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

37

Strana od-do

3939-3975

Kód UT WoS článku

000587719400041

EID výsledku v databázi Scopus

2-s2.0-85098535077