Let T be a symmetric statistic based on sample of size n drawn without replacement from a finite population of size N, where $N>n$. Assuming that the linear part of Hoeffding's decomposition of T is nondegenerate we construct a one term Edgeworth expansion for the distribution function of T and prove the validity of the expansion with the remainder $O(1/n^*)$ as $n^*\to \infty$, where $n^*=\min\{n,N-n\}$.
Publié le : 2002-07-14
Classification:
Edgeworth expansion,
finite population,
Hoeffding decomposition,
sampling without replacement,
62E20,
60F05
@article{1029867127,
author = {Bloznelis, M. and G\"otze, F.},
title = {An Edgeworth expansion for symmetric finite population statistics},
journal = {Ann. Probab.},
volume = {30},
number = {1},
year = {2002},
pages = { 1238-1265},
language = {en},
url = {http://dml.mathdoc.fr/item/1029867127}
}
Bloznelis, M.; Götze, F. An Edgeworth expansion for symmetric finite population statistics. Ann. Probab., Tome 30 (2002) no. 1, pp. 1238-1265. http://gdmltest.u-ga.fr/item/1029867127/