We introduce the notion of a multivariate local (and tail) empirical process indexed by sets and establish a number of functionals laws of the iterated logarithm for such processes. This leads to a unified methodology to study the almost sure behavior of various statistics which are local functionals of the empirical distribution. Such statistics include density estimators and the Bahadur-Kiefer representation.
Publié le : 1994-07-14
Classification:
Empirical measures,
strong laws,
functional laws of the iterated logarithm,
Donsker classes,
tail empirical processes,
density estimation,
Bahadur-Kiefer representation,
60F05,
60F15,
62E20,
62G30
@article{1176988617,
author = {Deheuvels, Paul and Mason, David M.},
title = {Functional Laws of the Iterated Logarithm for Local Empirical Processes Indexed by Sets},
journal = {Ann. Probab.},
volume = {22},
number = {4},
year = {1994},
pages = { 1619-1661},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988617}
}
Deheuvels, Paul; Mason, David M. Functional Laws of the Iterated Logarithm for Local Empirical Processes Indexed by Sets. Ann. Probab., Tome 22 (1994) no. 4, pp. 1619-1661. http://gdmltest.u-ga.fr/item/1176988617/