Asymptotic normality of extreme value estimators on C[0,1]

Abstract

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.