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Multivariate Tail Coefficients: Properties and Estimation

Multivariate tail coefficients are an important tool when investigating dependencies between extreme events for different components of a random vector. Although bivariate tail coefficients are well-studied, this is, to a lesser extent, the case for multivariate tail coefficients. This paper contrib...

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Detalles Bibliográficos
Autores principales: Gijbels, Irène, Kika, Vojtěch, Omelka, Marek
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7517269/
https://www.ncbi.nlm.nih.gov/pubmed/33286500
http://dx.doi.org/10.3390/e22070728
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author Gijbels, Irène
Kika, Vojtěch
Omelka, Marek
author_facet Gijbels, Irène
Kika, Vojtěch
Omelka, Marek
author_sort Gijbels, Irène
collection PubMed
description Multivariate tail coefficients are an important tool when investigating dependencies between extreme events for different components of a random vector. Although bivariate tail coefficients are well-studied, this is, to a lesser extent, the case for multivariate tail coefficients. This paper contributes to this research area by (i) providing a thorough study of properties of existing multivariate tail coefficients in the light of a set of desirable properties; (ii) proposing some new multivariate tail measurements; (iii) dealing with estimation of the discussed coefficients and establishing asymptotic consistency; and, (iv) studying the behavior of tail measurements with increasing dimension of the random vector. A set of illustrative examples is given, and practical use of the tail measurements is demonstrated in a data analysis with a focus on dependencies between stocks that are part of the EURO STOXX 50 market index.
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spelling pubmed-75172692020-11-09 Multivariate Tail Coefficients: Properties and Estimation Gijbels, Irène Kika, Vojtěch Omelka, Marek Entropy (Basel) Article Multivariate tail coefficients are an important tool when investigating dependencies between extreme events for different components of a random vector. Although bivariate tail coefficients are well-studied, this is, to a lesser extent, the case for multivariate tail coefficients. This paper contributes to this research area by (i) providing a thorough study of properties of existing multivariate tail coefficients in the light of a set of desirable properties; (ii) proposing some new multivariate tail measurements; (iii) dealing with estimation of the discussed coefficients and establishing asymptotic consistency; and, (iv) studying the behavior of tail measurements with increasing dimension of the random vector. A set of illustrative examples is given, and practical use of the tail measurements is demonstrated in a data analysis with a focus on dependencies between stocks that are part of the EURO STOXX 50 market index. MDPI 2020-06-30 /pmc/articles/PMC7517269/ /pubmed/33286500 http://dx.doi.org/10.3390/e22070728 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Gijbels, Irène
Kika, Vojtěch
Omelka, Marek
Multivariate Tail Coefficients: Properties and Estimation
title Multivariate Tail Coefficients: Properties and Estimation
title_full Multivariate Tail Coefficients: Properties and Estimation
title_fullStr Multivariate Tail Coefficients: Properties and Estimation
title_full_unstemmed Multivariate Tail Coefficients: Properties and Estimation
title_short Multivariate Tail Coefficients: Properties and Estimation
title_sort multivariate tail coefficients: properties and estimation
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7517269/
https://www.ncbi.nlm.nih.gov/pubmed/33286500
http://dx.doi.org/10.3390/e22070728
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