Estimates for the rate of strong Gaussian approximation for the sums of i.i.d.\ multidimensional random vectors
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 12, Tome 351 (2007), pp. 141-157
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The aim of this paper is to derive new optimal bounds for the rate of strong Gaussian approximation of sums of i.i.d. $\mathbb R^d$-valued random variables $\xi_j$ having finite moments of the form $\mathbb{E}\,H(\|\xi_j\|)$, where $H(x)$ is a monotone function growing not slower than $x^2$ and not faster than $e^{cx}$. We obtain some generalization and improvements of the results of U. Einmahl (1989).
@article{ZNSL_2007_351_a7,
author = {A. Yu. Zaitsev},
title = {Estimates for the rate of strong {Gaussian} approximation for the sums of i.i.d.\ multidimensional random vectors},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {141--157},
publisher = {mathdoc},
volume = {351},
year = {2007},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_351_a7/}
}
TY - JOUR AU - A. Yu. Zaitsev TI - Estimates for the rate of strong Gaussian approximation for the sums of i.i.d.\ multidimensional random vectors JO - Zapiski Nauchnykh Seminarov POMI PY - 2007 SP - 141 EP - 157 VL - 351 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_2007_351_a7/ LA - ru ID - ZNSL_2007_351_a7 ER -
%0 Journal Article %A A. Yu. Zaitsev %T Estimates for the rate of strong Gaussian approximation for the sums of i.i.d.\ multidimensional random vectors %J Zapiski Nauchnykh Seminarov POMI %D 2007 %P 141-157 %V 351 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_2007_351_a7/ %G ru %F ZNSL_2007_351_a7
A. Yu. Zaitsev. Estimates for the rate of strong Gaussian approximation for the sums of i.i.d.\ multidimensional random vectors. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 12, Tome 351 (2007), pp. 141-157. http://geodesic.mathdoc.fr/item/ZNSL_2007_351_a7/