We study orthogonal decomposition of symmetric statistics based on
samples drawn without replacement from finite populations. Several applications
to finite population statistics are given:we establish one-term Edgeworth
expansions for general asymptotically normal symmetric statistics, prove an
Efron-Stein inequality and the consistency of the jackknife esti- mator of
variance. Our expansions provide second order a.s. approximations to
Wu’s jackknife histogram.
Publié le : 2001-06-14
Classification:
ANOVA,
Hoeffding decomposition,
sampling without replacement,
finite population,
asymptotic expansion,
Edgeworth expansion,
stochastic expansion,
jackknife estimator of variance,
Efron-Stein inequality,
jackknife histogram,
62F20,
60F05
@article{1009210694,
author = {Bloznelis, M. and G\"otze, F.},
title = {Orthogonal decomposition of finite population statistics and its
applications to distributional asymptotics},
journal = {Ann. Statist.},
volume = {29},
number = {2},
year = {2001},
pages = { 899-917},
language = {en},
url = {http://dml.mathdoc.fr/item/1009210694}
}
Bloznelis, M.; Götze, F. Orthogonal decomposition of finite population statistics and its
applications to distributional asymptotics. Ann. Statist., Tome 29 (2001) no. 2, pp. 899-917. http://gdmltest.u-ga.fr/item/1009210694/