Four Examples of Lower Estimates in the Multi-Dimensional Central Limit Theorem

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Previous article Next article Four Examples of Lower Estimates in the Multi-Dimensional Central Limit TheoremV. V. SenatovV. V. Senatovhttps://doi.org/10.1137/1130098PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. V. Senatov, Uniform estimates of the rate of convergence in the multi-dimensional central limit theorem, Theory Prob. Appl., 25 (1980), 745–759 0471.60031 LinkGoogle Scholar[2] V. V. Senatov, On estimating the rate of convergence in the central limit theorem over a system of balls in $R^k$, Theory Prob. Appl., 28 (1983), 463–467 0569.60022 LinkGoogle Scholar[3] L. V. Osipov and , V. I. Rotar', On the convergence rate in the multidimensional and infinite-dimensional central limit theorems, Third International Vilnius Conference on Probability Theory and Mathematical Statistics, Summaries of Reports. V.2, Institute of Mathematics and Cybernetics of the Lithuanian Acad of Sciences, Vilnius, 1981, 97–98, (In Russian.) Google Scholar[4] V. V. Senatov, On the dependence of estimates of the convergence rate in the central limit theorem on the covariance operator of the summands, Theory Prob. Appl., 30 (1985), 156–159 Google Scholar[5] V. V. Yurinskii, On the accuracy of normal approximation of the probability of hitting a ball, Theory Prob. Appl., 27 (1982), 280–289 0565.60005 LinkGoogle Scholar[6] S. V. Nagaev, On accuracy of normal approximation for distribution of sum of independent Hilbert space-valued random variables, 4th USSR-Japan Symposium on Probability Theory and Mathematical Statistics, Abstracts of Communications. V.2, Metsniyereba. Tbilisi, 1982, 130– Google Scholar[7] F. Götze, Asymptotic expansions for bivariate von Mises functionals, Z. Wahrsch. Verw. Gebiete, 50 (1979), 333–355 81c:60025 0405.60009 CrossrefGoogle Scholar[8] V. V. Senatov, Some non-uniform estimates of the speed of convergence in the multi-dimensional central limit theorem, Theory Prob. Appl., 26 (1981), 657–669 0518.60025 LinkGoogle Scholar[9] V. V. Senatov, Some lower bounds for the rate of convergence in the central limit theorem in Hilbert space, Dokl. Akad. Nauk SSSR, 256 (1981), 1318–1322 82e:60011 0474.60007 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Some Approximation Problems in Statistics and Probability9 March 2013 Cross Ref On Estimates of the Rate of Convergence in the Central Limit Theorem in Multidimensional SpacesV. V. Senatov17 July 2006 | Theory of Probability & Its Applications, Vol. 37, No. 4AbstractPDF (259 KB)Some Remarks on Estimating the Rate of Convergence in the Central Limit Theorem in the Hilbert SpaceV. V. Senatov17 July 2006 | Theory of Probability & Its Applications, Vol. 36, No. 2AbstractPDF (614 KB)Some Remarks on Nonuniform Estimates of the Convergence RateV. V. Senatov17 July 2006 | Theory of Probability & Its Applications, Vol. 33, No. 3AbstractPDF (437 KB)A Regular Estimate of the Accuracy of Normal Approximation in Hilbert SpaceB. A. Zalesskii, V. V. Sazonov, and V. V. Ul’yanov28 July 2006 | Theory of Probability & Its Applications, Vol. 33, No. 4PDF (221 KB)Bibliography Cross Ref Volume 30, Issue 4| 1986Theory of Probability & Its Applications History Submitted:27 October 1983Published online:28 July 2006 InformationCopyright © 1986 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1130098Article page range:pp. 797-805ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics