Berry-Esseen theorems are proved in the multidimensional central limit theorem without using Fourier methods. An effective and simple estimate of the error in the CLT for sums and convex sets using Stein's method and induction is derived. Furthermore, the error in the CLT for multivariate functions of independent random elements is estimated extending results of van Zwet and Friedrich to the multivariate case.
Publié le : 1991-04-14
Classification:
Central limit theorem,
Berry-Esseen theorem,
Stein's method,
multivariate statistics,
60F05,
62H10
@article{1176990448,
author = {Gotze, F.},
title = {On the Rate of Convergence in the Multivariate CLT},
journal = {Ann. Probab.},
volume = {19},
number = {4},
year = {1991},
pages = { 724-739},
language = {en},
url = {http://dml.mathdoc.fr/item/1176990448}
}
Gotze, F. On the Rate of Convergence in the Multivariate CLT. Ann. Probab., Tome 19 (1991) no. 4, pp. 724-739. http://gdmltest.u-ga.fr/item/1176990448/