While the extreme value statistics for i.i.d data is well developed,
much less is known about the asymptotic behavior of statistical procedures in
the presence of dependence.We establish convergence of tail empirical processes
to Gaussianlimits for $\beta$-mixing stationary time series. As a consequence,
one obtains weighted approximations of the tail empirical quantile function
that is based on a random sequence with marginal distribution belonging to the
domain of attraction of an extreme value distribution. Moreover, the asymptotic
normality is concluded for a large class of estimators of the extreme value
index. These results are applied to stationary solutions of a general
stochastic difference equation.
Publié le : 2000-11-14
Classification:
ARCH-process,
dependent,
extreme value index,
Hill estimator,
invariance principle,
statistical tail functional,
stochastic difference equation,
tail empirical distribution function,
tail empirical quantile function,
time series,
$\beta$-mixing,
60F17,
62M10,
60G70,
62G20
@article{1019487617,
author = {Drees, Holger},
title = {Weighted approximations of tail processes for $\beta$-mixing
random variables},
journal = {Ann. Appl. Probab.},
volume = {10},
number = {2},
year = {2000},
pages = { 1274-1301},
language = {en},
url = {http://dml.mathdoc.fr/item/1019487617}
}
Drees, Holger. Weighted approximations of tail processes for $\beta$-mixing
random variables. Ann. Appl. Probab., Tome 10 (2000) no. 2, pp. 1274-1301. http://gdmltest.u-ga.fr/item/1019487617/