Matematičeskie zametki, Tome 23 (1978) no. 4, pp. 627-640
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L. V. Rozovskii. An estimate of the speed of convergence in the multidmensional central limit theorem without moment hypotheses. Matematičeskie zametki, Tome 23 (1978) no. 4, pp. 627-640. http://geodesic.mathdoc.fr/item/MZM_1978_23_4_a14/
@article{MZM_1978_23_4_a14,
author = {L. V. Rozovskii},
title = {An estimate of the speed of convergence in the multidmensional central limit theorem without moment hypotheses},
journal = {Matemati\v{c}eskie zametki},
pages = {627--640},
year = {1978},
volume = {23},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_4_a14/}
}
TY - JOUR
AU - L. V. Rozovskii
TI - An estimate of the speed of convergence in the multidmensional central limit theorem without moment hypotheses
JO - Matematičeskie zametki
PY - 1978
SP - 627
EP - 640
VL - 23
IS - 4
UR - http://geodesic.mathdoc.fr/item/MZM_1978_23_4_a14/
LA - ru
ID - MZM_1978_23_4_a14
ER -
%0 Journal Article
%A L. V. Rozovskii
%T An estimate of the speed of convergence in the multidmensional central limit theorem without moment hypotheses
%J Matematičeskie zametki
%D 1978
%P 627-640
%V 23
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_1978_23_4_a14/
%G ru
%F MZM_1978_23_4_a14
Let $X_1,\dots,X_n$ ($n\ge1$) be independent random vectors in $R_d$, $b$b be a vector in $R_d$. For an arbitrary Borel set $A\subset R_d$ we set \begin{gather*} P_n(A)=P\{X_1+\dots+X_n-b\in A\}, \\ \Delta_n(A)=|P_n(a)-\Phi(A)|, \end{gather*} where $\Phi(A)$ is the probability function of a standard normal vector in $R_d$. In this note are obtained estimates for $\Delta_n(A)$, where $A$ belongs to the class of convex Borel sets in $R_d$.
