A weighted localization of halfspace depth and its properties
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10366035" target="_blank" >RIV/00216208:11320/17:10366035 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmva.2017.02.008" target="_blank" >http://dx.doi.org/10.1016/j.jmva.2017.02.008</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmva.2017.02.008" target="_blank" >10.1016/j.jmva.2017.02.008</a>
Alternative languages
Result language
angličtina
Original language name
A weighted localization of halfspace depth and its properties
Original language description
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.
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/GA14-07234S" target="_blank" >GA14-07234S: Multivariate regression quantiles in econometrics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Multivariate Analysis
ISSN
0047-259X
e-ISSN
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Volume of the periodical
157
Issue of the periodical within the volume
157
Country of publishing house
US - UNITED STATES
Number of pages
17
Pages from-to
53-69
UT code for WoS article
000401299700005
EID of the result in the Scopus database
2-s2.0-85016462997