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

A. Yu Zaitsev

Research output

4 Citations (Scopus)

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 E H (∥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.

Translated title of the contributionОценки точности сильной гауссовской аппроксимации сумм независимых одинаково распределенных случайных векторов
Original languageEnglish
Pages (from-to)875-884
Number of pages10
JournalJournal of Mathematical Sciences
Volume152
Issue number6
DOIs
Publication statusPublished - 1 Aug 2008

Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)

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