### Abstract

For multivariate distributions in the domain of attraction of a max-stable distribution, the tail copula and the stable tail dependence function are equivalent ways to capture the dependence in the upper tail. The empirical versions of these functions are rank-based estimators whose inflated estimation errors are known to converge weakly to a Gaussian process that is similar in structure to the weak limit of the empirical copula process. We extend this multivariate result to continuous functional data by establishing the asymptotic normality of the estimators of the tail copula, uniformly over all finite subsets of at most D points (D fixed). As a special case we obtain the uniform asymptotic normality of all estimated upper tail dependence coefficients. The main tool for deriving the result is the uniform asymptotic normality of all the D-variate tail empirical processes. The proof of the main result is non-standard.

Original language | English |
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Place of Publication | Tilburg |

Publisher | CentER, Center for Economic Research |

Number of pages | 32 |

Volume | 2020-004 |

Publication status | Published - 3 Feb 2020 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2020-004 |

### Keywords

- extreme value statistics
- functional data
- tail empirical process
- tal dependence
- tial copula estimation
- uniform asymptotic normality

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## Cite this

Einmahl, J., & Segers, J. (2020).

*Empirical Tail Copulas for Functional Data*. (CentER Discussion Paper; Vol. 2020-004). CentER, Center for Economic Research.