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Open AccessArticle

Multivariate Tail Coefficients: Properties and Estimation

Department of Mathematics and Leuven Statistics Research Center (LStat), KU Leuven, 3001 Leuven, Belgium
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;
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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