Suppose that $U$ is a $U$-statistic of degree 2 based on a simple random sample of size $n$ selected without replacement from a finite population of $N$ elements. A bound for the difference between the distribution function of a standardized version of $U$ and its single-term Edgeworth expansion is given. We apply these results to obtain an Edgeworth expansion for the variance estimator in a finite population. Some simulation results are reported in this case.
Publié le : 1990-01-14
Classification:
$U$-statistics,
Edgeworth expansion,
Berry-Esseen bound,
sampling from a finite population,
60F05
@article{1176990955,
author = {Kokic, P. N. and Weber, N. C.},
title = {An Edgeworth Expansion for $U$-Statistics Based on Samples from Finite Populations},
journal = {Ann. Probab.},
volume = {18},
number = {4},
year = {1990},
pages = { 390-404},
language = {en},
url = {http://dml.mathdoc.fr/item/1176990955}
}
Kokic, P. N.; Weber, N. C. An Edgeworth Expansion for $U$-Statistics Based on Samples from Finite Populations. Ann. Probab., Tome 18 (1990) no. 4, pp. 390-404. http://gdmltest.u-ga.fr/item/1176990955/