Asymptotic Normality of Extreme Value Estimators on C[0,1]

Consider n i.i.d. random elements on C[0; 1].We show that under an appropriate strengthening of the domain of attraction condition natural estimators of the extreme-value index, which is now a continuous function, and the normalizing functions have a Gaussian process as limiting distribution.A key tool is the weak convergence of a weighted tail empirical process, which makes it possible to obtain the results uniformly on [0; 1].Detailed examples are also presented.