Uniform convergence rates for the approximated halfspace and projection depth
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Uniform convergence rates for the approximated halfspace and projection depth
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10103 - Statistics and probability
Result continuities
Project
<a href="/en/project/GJ19-16097Y" target="_blank" >GJ19-16097Y: Geometric aspects of mathematical statistics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Journal of Statistics
ISSN
1935-7524
e-ISSN
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Volume of the periodical
14
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
37
Pages from-to
3939-3975
UT code for WoS article
000587719400041
EID of the result in the Scopus database
2-s2.0-85098535077