Statistical properties of partially observed integrated functional depths

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10507217" target="_blank" >RIV/00216208:11320/25:10507217 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ZQw_HPq1fQ" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ZQw_HPq1fQ</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11749-024-00954-6" target="_blank" >10.1007/s11749-024-00954-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Statistical properties of partially observed integrated functional depths

Popis výsledku v původním jazyce

Integrated functional depths (IFDs) present a versatile toolbox of methods introducing notions of ordering, quantiles, and rankings into a functional data analysis context. They provide fundamental tools for nonparametric inference of infinite-dimensional data. Recently, the literature has extended IFDs to address the challenges posed by partial observability of functional data, commonly encountered in practice. That resulted in the development of partially observed integrated functional depths (POIFDs). POIFDs have demonstrated good empirical results in simulated experiments and real problems. However, there are still no theoretical results in line with the state of the art of IFDs. This article addresses this gap by providing theoretical support for POIFDs, including (i) uniform consistency of their sample versions, (ii) weak continuity with respect to the underlying probability measure, and (iii) uniform consistency for discretely observed functional data. Finally, we present a sensitivity analysis that evaluates how our theoretical results are affected by violations of the main assumptions.

Název v anglickém jazyce

Statistical properties of partially observed integrated functional depths

Popis výsledku anglicky

Integrated functional depths (IFDs) present a versatile toolbox of methods introducing notions of ordering, quantiles, and rankings into a functional data analysis context. They provide fundamental tools for nonparametric inference of infinite-dimensional data. Recently, the literature has extended IFDs to address the challenges posed by partial observability of functional data, commonly encountered in practice. That resulted in the development of partially observed integrated functional depths (POIFDs). POIFDs have demonstrated good empirical results in simulated experiments and real problems. However, there are still no theoretical results in line with the state of the art of IFDs. This article addresses this gap by providing theoretical support for POIFDs, including (i) uniform consistency of their sample versions, (ii) weak continuity with respect to the underlying probability measure, and (iii) uniform consistency for discretely observed functional data. Finally, we present a sensitivity analysis that evaluates how our theoretical results are affected by violations of the main assumptions.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

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

2025

Kód důvěrnosti údajů

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

Název periodika

Test

ISSN

1133-0686

e-ISSN

1863-8260

Svazek periodika

34

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

ES - Španělské království

Počet stran výsledku

26

Strana od-do

125-150

Kód UT WoS článku

001359305900001

EID výsledku v databázi Scopus

2-s2.0-105001078694