Empirical tail copulas for functional data

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