Geodesic
On the estimate of the rate of convergence with respect to the system of balls in the central limit theorem in $R^k$
Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 2, pp. 440-445

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain an estimate of the order $O(n^{-1/2)}$ for the rate of convergence with respect to the balls in the central limit theorem in $R^k$. The main part of the estimate does not depend on the dimensional parameter $k$. This estimate accounts the closeness of the distributions of summands to the normal distribution. 
@article{TVP_1983_28_2_a21,
     author = {V. V. Senatov},
     title = {On the estimate of the rate of convergence with respect to the system of balls in the central limit theorem in $R^k$},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {440--445},
     publisher = {mathdoc},
     volume = {28},
     number = {2},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1983_28_2_a21/}
}
TY  - JOUR
AU  - V. V. Senatov
TI  - On the estimate of the rate of convergence with respect to the system of balls in the central limit theorem in $R^k$
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1983
SP  - 440
EP  - 445
VL  - 28
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_1983_28_2_a21/
LA  - ru
ID  - TVP_1983_28_2_a21
ER  - 
%0 Journal Article
%A V. V. Senatov
%T On the estimate of the rate of convergence with respect to the system of balls in the central limit theorem in $R^k$
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1983
%P 440-445
%V 28
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_1983_28_2_a21/
%G ru
%F TVP_1983_28_2_a21
V. V. Senatov. On the estimate of the rate of convergence with respect to the system of balls in the central limit theorem in $R^k$. Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 2, pp. 440-445. http://geodesic.mathdoc.fr/item/TVP_1983_28_2_a21/