Characterizations of laws of the iterated logarithm for the supremum of weighted uniform $\lbrack 0, 1\rbrack^d$ empirical processes taken over increasingly smaller regions near the origin are obtained. These results have proven to be a valuable tool in the derivation of laws of the iterated logarithm for sums of extreme values. They also constitute a further continuation of the study of the almost sure behavior of weighted uniform empirical processes, which in a certain sense was begun by Csaki.
Publié le : 1988-01-14
Classification:
Order statistics,
weighted empirical processes,
laws of the iterated logarithm,
60F15,
60G17
@article{1176991889,
author = {Einmahl, John H. J. and Mason, David M.},
title = {Laws of the Iterated Logarithm in the Tails for Weighted Uniform Empirical Processes},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 126-141},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991889}
}
Einmahl, John H. J.; Mason, David M. Laws of the Iterated Logarithm in the Tails for Weighted Uniform Empirical Processes. Ann. Probab., Tome 16 (1988) no. 4, pp. 126-141. http://gdmltest.u-ga.fr/item/1176991889/