# Extreme TiDE Seminar

## 11 March 2020 at (Tilburg University).

**Title:** *Testing the equality of tail dependence structures of two multivariate samples *

**Abstract:** Consider two i.i.d. samples of possibly different sizes, independently generated from d-variate distribution functions $F$ and $F'$. Suppose the two distributions lie in the maximum domains of attraction of extreme value distributions $G$ and $G'$, with associated tail copulas $R$ and $R'$. We propose a procedure for constructing asymptotically distribution-free tests for the equality of $R$ and $R'$. This is a joint work with John Einmahl and Roger Laeven.
### 15:45-16:00 Coffee break

**Title:** *Empirical tail copulas for functional data*

**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 co-efficients. 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.
This is a joint work with John Einmahl.
### 17:00-18:00 Drinks and Snacks

The seminar will take place at room K 1206, Koopmans Building, Tilburg University. Full address: Warandelaan 2, 5037 AB Tilburg.