Integrated depth for functional data: statistical properties and consistency

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10329863" target="_blank" >RIV/00216208:11320/16:10329863 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1051/ps/2016005" target="_blank" >http://dx.doi.org/10.1051/ps/2016005</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1051/ps/2016005" target="_blank" >10.1051/ps/2016005</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Integrated depth for functional data: statistical properties and consistency

Popis výsledku v původním jazyce

Several depths suitable for infinite-dimensional functional data that are available in the literature are of the form of an integral of a finite-dimensional depth function. These functionals are characterized by projecting functions into low-dimensional spaces, taking finite-dimensional depths of the projected quantities, and finally integrating these projected marginal depths over a preset collection of projections. In this paper, a general class of integrated depths for functions is considered. Several depths for functional data proposed in the literature during the last decades are members of this general class. A comprehensive study of its most important theoretical properties, including measurability and consistency, is given. It is shown that many, but not all, properties of the integrated depth are shared with the finite-dimensional depth that constitutes its building block. Some pending measurability issues connected with all integrated depth functionals are resolved, a broad new notion of symmetry for functional data is proposed, and difficulties with respect to consistency results are identified. A general universal consistency result for the sample depth version, and for the generalized median, for integrated depth for functions is derived

Název v anglickém jazyce

Integrated depth for functional data: statistical properties and consistency

Popis výsledku anglicky

Several depths suitable for infinite-dimensional functional data that are available in the literature are of the form of an integral of a finite-dimensional depth function. These functionals are characterized by projecting functions into low-dimensional spaces, taking finite-dimensional depths of the projected quantities, and finally integrating these projected marginal depths over a preset collection of projections. In this paper, a general class of integrated depths for functions is considered. Several depths for functional data proposed in the literature during the last decades are members of this general class. A comprehensive study of its most important theoretical properties, including measurability and consistency, is given. It is shown that many, but not all, properties of the integrated depth are shared with the finite-dimensional depth that constitutes its building block. Some pending measurability issues connected with all integrated depth functionals are resolved, a broad new notion of symmetry for functional data is proposed, and difficulties with respect to consistency results are identified. A general universal consistency result for the sample depth version, and for the generalized median, for integrated depth for functions is derived

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

ESAIM - Probability and Statistics

ISSN

1292-8100

e-ISSN

—

Svazek periodika

20

Číslo periodika v rámci svazku

14.7.2016

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

36

Strana od-do

95-130

Kód UT WoS článku

000390777500006

EID výsledku v databázi Scopus

2-s2.0-84978630466