A general procedure for multistage modification of pivotal statistics is developed to improve the normal approximation. Bootstrapping a first stage modified statistic is shown to be equivalent, in terms of asymptotic order, to the normal approximation of a second stage modification. Explicit formulae are given for some basic cases involving independent random samples and samples drawn without replacement. The Hodges-Lehmann deficiency is calculated to compare the regular $t$-statistic with its one-step correction.
Publié le : 1985-03-14
Classification:
Pivotal statistics,
confidence intervals,
hypothesis testing,
Edgeworth expansions,
bootstrap procedure,
random sampling without replacement,
62E20,
62G10,
62G15,
62G20
@article{1176346580,
author = {Abramovitch, Lavy and Singh, Kesar},
title = {Edgeworth Corrected Pivotal Statistics and the Bootstrap},
journal = {Ann. Statist.},
volume = {13},
number = {1},
year = {1985},
pages = { 116-132},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346580}
}
Abramovitch, Lavy; Singh, Kesar. Edgeworth Corrected Pivotal Statistics and the Bootstrap. Ann. Statist., Tome 13 (1985) no. 1, pp. 116-132. http://gdmltest.u-ga.fr/item/1176346580/