Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 2, pp. 369-373
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T. L. Malevič; В. Abdalimov. More precise form of the central limit theorem for $U$-statistics of $m$-dependent variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 2, pp. 369-373. http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a20/
@article{TVP_1982_27_2_a20,
author = {T. L. Malevi\v{c} and {\CYRV}. Abdalimov},
title = {More precise form of the central limit theorem for $U$-statistics of $m$-dependent variables},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {369--373},
year = {1982},
volume = {27},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a20/}
}
TY - JOUR
AU - T. L. Malevič
AU - В. Abdalimov
TI - More precise form of the central limit theorem for $U$-statistics of $m$-dependent variables
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1982
SP - 369
EP - 373
VL - 27
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a20/
LA - ru
ID - TVP_1982_27_2_a20
ER -
%0 Journal Article
%A T. L. Malevič
%A В. Abdalimov
%T More precise form of the central limit theorem for $U$-statistics of $m$-dependent variables
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1982
%P 369-373
%V 27
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a20/
%G ru
%F TVP_1982_27_2_a20
Let $X_1,X_2,\dots$ be a stationary sequence of $m$-dependent random variables and let $\Phi(x_1,\dots,x_r)$ be a symmetric function. For the distribution of the $U$-statistics $$ U_n=(C_n^r)^{-1}\sum_{1\le i_1<\dots<i_r\le n}\Phi(X_{i_1},\dots,X_{i_r}) $$ the rate of convergence to the normal law is investigated.
