Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part IX, Tome 142 (1985), pp. 59-67
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V. A. Egorov. The central limit theorem under the absence of extremal absolute order statistics. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part IX, Tome 142 (1985), pp. 59-67. http://geodesic.mathdoc.fr/item/ZNSL_1985_142_a5/
@article{ZNSL_1985_142_a5,
author = {V. A. Egorov},
title = {The central limit theorem under the absence of extremal absolute order statistics},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {59--67},
year = {1985},
volume = {142},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_142_a5/}
}
TY - JOUR
AU - V. A. Egorov
TI - The central limit theorem under the absence of extremal absolute order statistics
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1985
SP - 59
EP - 67
VL - 142
UR - http://geodesic.mathdoc.fr/item/ZNSL_1985_142_a5/
LA - ru
ID - ZNSL_1985_142_a5
ER -
%0 Journal Article
%A V. A. Egorov
%T The central limit theorem under the absence of extremal absolute order statistics
%J Zapiski Nauchnykh Seminarov POMI
%D 1985
%P 59-67
%V 142
%U http://geodesic.mathdoc.fr/item/ZNSL_1985_142_a5/
%G ru
%F ZNSL_1985_142_a5
One finds conditions for the relation $\Delta_{n,r}=o(1)=\nabla_{n,r}$, где $\Delta_{n,r}=\sup_x|P\Big(\frac{S_{n,r}}{a_n}, $S_{n,r}=X_{(1)}+\dots+X_{(n-r)}$, $X_{(1)},\dots,X_{(n)}$ are the absolute order statistics for a repeated sample from a symmetric distribution.
