For $U$-Statistics and von Mises' differentiable statistical functions, when the regular functional is stationary of order zero, almost sure convergence to appropriate Wiener processes is studied. A second almost sure invariance principle, particularly useful in the context of the law of iterated logarithm and the probability of moderate deviations, is also established.
Publié le : 1974-03-14
Classification:
Almost sure convergence,
invariance principle,
Wiener process,
$U$-statistics,
von Mises' functionals,
law of iterated logarithm and probability of moderate deviations,
60B10,
60F15,
62E20
@article{1176342675,
author = {Sen, Pranab Kumar},
title = {Almost Sure Behaviour of $U$-Statistics and Von Mises' Differentiable Statistical Functions},
journal = {Ann. Statist.},
volume = {2},
number = {1},
year = {1974},
pages = { 387-395},
language = {en},
url = {http://dml.mathdoc.fr/item/1176342675}
}
Sen, Pranab Kumar. Almost Sure Behaviour of $U$-Statistics and Von Mises' Differentiable Statistical Functions. Ann. Statist., Tome 2 (1974) no. 1, pp. 387-395. http://gdmltest.u-ga.fr/item/1176342675/