Flexible integrated functional depths
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10419111" target="_blank" >RIV/00216208:11320/21:10419111 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=TOX7s3swmF" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=TOX7s3swmF</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3150/20-BEJ1254" target="_blank" >10.3150/20-BEJ1254</a>
Alternative languages
Result language
angličtina
Original language name
Flexible integrated functional depths
Original language description
This paper develops a new class of functional depths. A generic member of this class is coined Jth order kth moment integrated depth. It is based on the distribution of the cross-sectional halfspace depth of a function in the marginal evaluations (in time) of the random process. Asymptotic properties of the proposed depths are provided: we show that they are uniformly consistent and satisfy an inequality related to the law of the iterated logarithm. Moreover, limiting distributions are derived under mild regularity assumptions. The versatility displayed by the new class of depths makes them particularly amenable for capturing important features of functional distributions. This is illustrated in supervised learning, where we show that the corresponding maximum depth classifiers outperform classical competitors.
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
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Bernoulli
ISSN
1350-7265
e-ISSN
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Volume of the periodical
27
Issue of the periodical within the volume
1
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
29
Pages from-to
673-701
UT code for WoS article
000592642200027
EID of the result in the Scopus database
2-s2.0-85097471887