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Open AccessArticle

Multivariate Tail Coefficients: Properties and Estimation

1
Department of Mathematics and Leuven Statistics Research Center (LStat), KU Leuven, 3001 Leuven, Belgium
2
Faculty of Mathematics and Physics, Department of Probability and Mathematical Statistics, Charles University, 186 75 Prague, Czech Republic
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(7), 728; https://doi.org/10.3390/e22070728
Received: 3 April 2020 / Revised: 22 June 2020 / Accepted: 25 June 2020 / Published: 30 June 2020
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.
Keywords: archimedean copula; consistency; estimation; extreme-value copula; tail dependency; multivariate analysis archimedean copula; consistency; estimation; extreme-value copula; tail dependency; multivariate analysis
MDPI and ACS Style

Gijbels, I.; Kika, V.; Omelka, M. Multivariate Tail Coefficients: Properties and Estimation. Entropy 2020, 22, 728.

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