Athreya showed that the bootstrap distribution of a sum of infinite variance random variables did not (with probability 1) tend weakly to a fixed distribution but instead tended in distribution to a random distribution. In this paper, we give a different proof of Athreya's result motivated by a heuristic large sample representation of the bootstrap distribution.
Publié le : 1989-09-14
Classification:
Bootstrap,
stable law,
random probability measures,
weak convergence,
62E20,
60B05,
60G57
@article{1176347262,
author = {Knight, Keith},
title = {On the Bootstrap of the Sample Mean in the Infinite Variance Case},
journal = {Ann. Statist.},
volume = {17},
number = {1},
year = {1989},
pages = { 1168-1175},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347262}
}
Knight, Keith. On the Bootstrap of the Sample Mean in the Infinite Variance Case. Ann. Statist., Tome 17 (1989) no. 1, pp. 1168-1175. http://gdmltest.u-ga.fr/item/1176347262/