We derive invariance principles for processes associated with symmetric statistics of arbitrary order. Using a Poisson sample size, such processes can be viewed as functionals of a Poisson Point Process. Properly normalized, these functionals converge in distribution to functionals of a Gaussian random measure associated with the distribution of the observations. We thus obtain a natural description of the limiting process in terms of multiple Wiener integrals. The results are used to derive asymptotic expansions of processes arising from arbitrary square integrable $U$-statistics.
Publié le : 1984-06-14
Classification:
Symmetric statistics,
invariance principle,
multiple Wiener integral,
$U$-statistics,
Hermite polynomials,
60F17,
62E20,
62G05,
60G99,
60K99
@article{1176346501,
author = {Mandelbaum, Avi and Taqqu, Murad S.},
title = {Invariance Principle for Symmetric Statistics},
journal = {Ann. Statist.},
volume = {12},
number = {1},
year = {1984},
pages = { 483-496},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346501}
}
Mandelbaum, Avi; Taqqu, Murad S. Invariance Principle for Symmetric Statistics. Ann. Statist., Tome 12 (1984) no. 1, pp. 483-496. http://gdmltest.u-ga.fr/item/1176346501/