Gijbels Irène, Kika Vojtěch, Omelka Marek
Department of Mathematics and Leuven Statistics Research Center (LStat), KU Leuven, 3001 Leuven, Belgium.
Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University, 186 75 Prague, Czech Republic.
Entropy (Basel). 2020 Jun 30;22(7):728. doi: 10.3390/e22070728.
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.
在研究随机向量不同分量的极端事件之间的相关性时，多元尾部系数是一个重要工具。尽管二元尾部系数已得到充分研究，但多元尾部系数在较小程度上也是如此。本文通过以下方式对该研究领域做出贡献：（i）根据一组理想性质对现有多元尾部系数的性质进行深入研究；（ii）提出一些新的多元尾部度量；（iii）处理所讨论系数的估计并建立渐近一致性；以及（iv）研究随着随机向量维度增加尾部度量的行为。给出了一组说明性示例，并在数据分析中展示了尾部度量的实际应用，重点关注欧洲斯托克50指数市场指数中股票之间的相关性。
