Generalized Hadamard differentiability of the copula mapping and its applications

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Generalized Hadamard differentiability of the copula mapping and its applications
Original language description
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<acute accent> and Wegkamp (2004) and (under less strict assumptions) in B & 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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10103 - Statistics and probability

Project
<a href="/en/project/GA22-11867S" target="_blank" >GA22-11867S: Advanced operational research methods for optimal decision-making in waste management</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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