Bootstrap distributional limit theorems for $U$ and $V$ statistics are proved. They hold a.s., under weak moment conditions and without restrictions on the bootstrap sample size (as long as it tends to $\infty$), regardless of the degree of degeneracy of $U$ and $V$. A testing procedure based on these results is outlined.
Publié le : 1992-06-14
Classification:
Bootstrap,
$U$-statistics,
von Mises functionals,
62E20,
60F05,
62F05
@article{1176348650,
author = {Arcones, Miguel A. and Gine, Evarist},
title = {On the Bootstrap of $U$ and $V$ Statistics},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 655-674},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348650}
}
Arcones, Miguel A.; Gine, Evarist. On the Bootstrap of $U$ and $V$ Statistics. Ann. Statist., Tome 20 (1992) no. 1, pp. 655-674. http://gdmltest.u-ga.fr/item/1176348650/