Generalized Hadamard differentiability of the copula mapping and its applications

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10506646" target="_blank" >RIV/00216208:11320/25:10506646 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=eej9smCfrB" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=eej9smCfrB</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3150/24-BEJ1777" target="_blank" >10.3150/24-BEJ1777</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Generalized Hadamard differentiability of the copula mapping and its applications

Popis výsledku v původním jazyce

We consider the copula mapping, which maps a joint cumulative distribution function to the corresponding copula. Its Hadamard differentiability was shown in van der Vaart and Wellner (1996), Fermanian, Radulovic&lt;acute accent&gt; and Wegkamp (2004) and (under less strict assumptions) in B &amp; uuml;cher and Volgushev (2013). This differentiability result has proved to be a powerful tool to show the weak convergence of empirical copula processes in various settings using the functional delta method. We state a generalization of the Hadamard differentiability results and illustrate how it can be used for the derivations of asymptotic expansions and the weak convergence of empirical copula processes in the presence of covariates. The usefulness of this result is illustrated on several applications which include a multidimensional functional linear model, where the copula of the error vector describes the dependency between the components of the vector of observations, given the functional covariate.

Název v anglickém jazyce

Generalized Hadamard differentiability of the copula mapping and its applications

Popis výsledku anglicky

We consider the copula mapping, which maps a joint cumulative distribution function to the corresponding copula. Its Hadamard differentiability was shown in van der Vaart and Wellner (1996), Fermanian, Radulovic&lt;acute accent&gt; and Wegkamp (2004) and (under less strict assumptions) in B &amp; uuml;cher and Volgushev (2013). This differentiability result has proved to be a powerful tool to show the weak convergence of empirical copula processes in various settings using the functional delta method. We state a generalization of the Hadamard differentiability results and illustrate how it can be used for the derivations of asymptotic expansions and the weak convergence of empirical copula processes in the presence of covariates. The usefulness of this result is illustrated on several applications which include a multidimensional functional linear model, where the copula of the error vector describes the dependency between the components of the vector of observations, given the functional covariate.

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/GA22-11867S" target="_blank" >GA22-11867S: Pokročilé metody operačního výzkumu pro optimální rozhodování v odpadovém hospodářství</a><br>

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

Bernoulli

ISSN

1350-7265

e-ISSN

1573-9759

Svazek periodika

31

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

24

Strana od-do

1451-1474

Kód UT WoS článku

001426603800024

EID výsledku v databázi Scopus

2-s2.0-85218783513