Data depth for measurable noisy random functions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10399730" target="_blank" >RIV/00216208:11320/19:10399730 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=BNNqCSHoMf" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=BNNqCSHoMf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmva.2018.11.003" target="_blank" >10.1016/j.jmva.2018.11.003</a>
Alternative languages
Result language
angličtina
Original language name
Data depth for measurable noisy random functions
Original language description
In the literature on data depth applicable to random functions, it is usually assumed that the trajectories of all the random curves are continuous, known at each point of the domain, and observed exactly. These assumptions turn out to be unrealistic in practice, as the functions are often observed only on a finite grid of time points, and in the presence of measurement errors. In this work, we provide the necessary theoretical background enabling the extension of the statistical methodology based on data depth to measurable (not necessarily continuous) random functions observed within the latter framework. It is shown that even if the random functions are discontinuous, observed discretely, and contaminated with additive noise, many common depth functionals maintain the fine consistency properties valid in the ideal case of completely observed noiseless functions. For the integrated depth for functions, we provide uniform rates of convergence over the space of integrable functions. (C) 2018 Elsevier Inc. All rights reserved.
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/GJ18-00522Y" target="_blank" >GJ18-00522Y: Advanced Econometric Models for Option Pricing – AdEMOP</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
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
170
Issue of the periodical within the volume
March
Country of publishing house
US - UNITED STATES
Number of pages
20
Pages from-to
95-114
UT code for WoS article
000457205300008
EID of the result in the Scopus database
2-s2.0-85057727651