Wichura (1969) studied an invariance principle for partial sums of a multi-dimensional array of independent random variables. It is shown that a similar invariance principle holds for a broad class of generalized $U$-statistics for which the different terms in the partial sums are not independent. Weak convergence of generalized $U$-statistics for random sample sizes is also studied. The case of (generalized) von Mises' functional is treated briefly.
Publié le : 1974-02-14
Classification:
$D \{\lbrack 0, 1 \rbrack^c\}$ space,
Generalized $U$-statistics,
invariance principle,
Gaussian processes,
relative compactness,
random indices,
Von Mises' differentiable statistical functions and weak convergence,
60B10,
60G99
@article{1176996754,
author = {Sen, Pranab Kumar},
title = {Weak Convergence of Generalized $U$-Statistics},
journal = {Ann. Probab.},
volume = {2},
number = {6},
year = {1974},
pages = { 90-102},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996754}
}
Sen, Pranab Kumar. Weak Convergence of Generalized $U$-Statistics. Ann. Probab., Tome 2 (1974) no. 6, pp. 90-102. http://gdmltest.u-ga.fr/item/1176996754/