A Berry-Esseen theorem for the rate of convergence of general nonlinear multivariate sampling statistics with normal limit distribution is derived via a multivariate extension of Stein's method. The result generalizes in particular previous results of Bolthausen for one-dimensional linear rank statistics, one-dimensional results of van Zwet and Friedrich for general functions of independent random elements and provides convergence bounds for general multivariate sampling statistics without restrictions on the sampling proportions.
Publié le : 1993-12-14
Classification:
Berry-Esseen theorem,
multivariate central limit theorem,
rank statistics,
sampling statistics,
60F05,
62E20
@article{1176349393,
author = {Bolthausen, Erwin and Gotze, Friedrich},
title = {The Rate of Convergence for Multivariate Sampling Statistics},
journal = {Ann. Statist.},
volume = {21},
number = {1},
year = {1993},
pages = { 1692-1710},
language = {en},
url = {http://dml.mathdoc.fr/item/1176349393}
}
Bolthausen, Erwin; Gotze, Friedrich. The Rate of Convergence for Multivariate Sampling Statistics. Ann. Statist., Tome 21 (1993) no. 1, pp. 1692-1710. http://gdmltest.u-ga.fr/item/1176349393/