Data depth for measurable noisy random functions

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Data depth for measurable noisy random functions

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Data depth for measurable noisy random functions

Popis výsledku anglicky

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.

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/GJ18-00522Y" target="_blank" >GJ18-00522Y: Pokročilé Ekonometrické Modely pro Oceňování Opcí – AdEMOP</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Journal of Multivariate Analysis

ISSN

0047-259X

e-ISSN

—

Svazek periodika

170

Číslo periodika v rámci svazku

March

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

20

Strana od-do

95-114

Kód UT WoS článku

000457205300008

EID výsledku v databázi Scopus

2-s2.0-85057727651