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Estimates for the rate of strong Gaussian approximation for sums of i.i.d. multidimensional random vectors

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Abstract

The aim of this paper is to derive new optimal bounds for the rate of strong Gaussian approximation of sums of i.i.d. R d-valued random variables ξj that have finite moments of the form EH (‖ξj‖), where H (x) is a monotone function growing not slower than x2 and not faster than ecx. We obtain some generalization and improvements of results of U. Einmahl (1989). Bibliography: 28 titles.

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  1. St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg, Russia

    A. Yu. Zaitsev

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Correspondence to A. Yu. Zaitsev.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 351, 2007, pp. 141–158.

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Zaitsev, A.Y. Estimates for the rate of strong Gaussian approximation for sums of i.i.d. multidimensional random vectors. J Math Sci 152, 875–884 (2008). https://doi.org/10.1007/s10958-008-9105-4

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