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.
Publié le : 2006-02-14
Classification:
Estimation,
extreme value index,
infinite-dimensional extremes,
weak convergence on C[0,1],
62G32,
62G30,
62G05,
60G70,
60F17
@article{1146576271,
author = {Einmahl, John H. J. and Lin, Tao},
title = {Asymptotic normality of extreme value estimators on C[0,1]},
journal = {Ann. Statist.},
volume = {34},
number = {1},
year = {2006},
pages = { 469-492},
language = {en},
url = {http://dml.mathdoc.fr/item/1146576271}
}
Einmahl, John H. J.; Lin, Tao. Asymptotic normality of extreme value estimators on C[0,1]. Ann. Statist., Tome 34 (2006) no. 1, pp. 469-492. http://gdmltest.u-ga.fr/item/1146576271/