Suppose that U is a U-statistic of degree 2 based on N random observations drawn without replacement from a finite population. For the distribution of a standardized version of U we construct an Edgeworth expansion with remainder O(N-1) provided that the linear part of the statistic satisfies a Cramér type condition.
Publié le : 2000-08-14
Classification:
central limit theorem,
Edgeworth expansion,
finite population,
U-statistic,
sampling without replacement
@article{1081449604,
author = {Bloznelis, Mindaugas and G\"otze, Friedrich},
title = {An Edgeworth expansion for finite-population U-statistics},
journal = {Bernoulli},
volume = {6},
number = {6},
year = {2000},
pages = { 729-760},
language = {en},
url = {http://dml.mathdoc.fr/item/1081449604}
}
Bloznelis, Mindaugas; Götze, Friedrich. An Edgeworth expansion for finite-population U-statistics. Bernoulli, Tome 6 (2000) no. 6, pp. 729-760. http://gdmltest.u-ga.fr/item/1081449604/