It is proved that $EX^2 < \infty$ is necessary for a very mild form of the bootstrap of the mean to work a.s. and that $X$ must be in the domain of attraction of the normal law if a.s. is weakened to "in probability."
Publié le : 1989-06-14
Classification:
Bootstrap (of the mean),
central limit theorem,
62E20,
62F12,
60F05
@article{1176347134,
author = {Gine, Evarist and Zinn, Joel},
title = {Necessary Conditions for the Bootstrap of the Mean},
journal = {Ann. Statist.},
volume = {17},
number = {1},
year = {1989},
pages = { 684-691},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347134}
}
Gine, Evarist; Zinn, Joel. Necessary Conditions for the Bootstrap of the Mean. Ann. Statist., Tome 17 (1989) no. 1, pp. 684-691. http://gdmltest.u-ga.fr/item/1176347134/