An Edgeworth expansion with remainder $o(N^{-1})$ is established for a $U$-statistic with a kernel $h$ of degree 2. The assumptions involved appear to be very mild; in particular, the common distribution of the summands $h(X_i, X_j)$ is not assumed to be smooth.
Publié le : 1986-12-14
Classification:
Edgeworth expansion,
second order asymptotics,
$U$-statistics,
62E20,
60F05
@article{1176350170,
author = {Bickel, P. J. and Gotze, F. and van Zwet, W. R.},
title = {The Edgeworth Expansion for $U$-Statistics of Degree Two},
journal = {Ann. Statist.},
volume = {14},
number = {2},
year = {1986},
pages = { 1463-1484},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350170}
}
Bickel, P. J.; Gotze, F.; van Zwet, W. R. The Edgeworth Expansion for $U$-Statistics of Degree Two. Ann. Statist., Tome 14 (1986) no. 2, pp. 1463-1484. http://gdmltest.u-ga.fr/item/1176350170/