2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131068Consider $n$ 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.Published at http://dx.doi.org/10.1214/009053605000000831 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)Statistics Theory62G32, 62G30, 62G05 (Primary) 60G70, 60F17 (Secondary)text