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.
"Asymptotic normality of extreme value estimators on C[0,1]." Ann. Statist. 34 (1) 469 - 492, February 2006. https://doi.org/10.1214/009053605000000831