Estimate of the Accuracy of Normal Approximation in Hilbert Space

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Previous article Next article Estimate of the Accuracy of Normal Approximation in Hilbert SpaceB. A. ZalesskiiB. A. Zalesskiihttps://doi.org/10.1137/1127031PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. V. Sazonov, Normal approximation—some recent advances, Lecture Notes in Mathematics, Vol. 879, Springer-Verlag, Berlin, 1981vii+105 83g:60035 0462.60006 CrossrefGoogle Scholar[2] F. Götze, Asymptotic expansions for bivariate von Mises functionals, Z. Wahrsch. Verw. Gebiete, 50 (1979), 333–355 81c:60025 0405.60009 CrossrefGoogle Scholar[3] F. Götze, Convergence rate in the central limit theorem in Hilbert space, 14th European Meeting of Statisticians, Abstracts, Wroclaw, 1981, 35– Google Scholar[4] V. V. Yurinskii, On the infinite-dimensional version of S. N. Bernshtein's inequalities, Theory. Prob. Appl., 15 (1970), 108–109 LinkGoogle Scholar[5] V. V. Petrov, Sums of independent random variables, Springer-Verlag, New York, 1975x+346 52:9335 0322.60042 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Rates of convergence for the Nummelin conditional weak law of large numbersStochastic Processes and their Applications, Vol. 98, No. 2 Cross Ref Asymptotic expansions in the integral and local limit theorems in banach spaces with applications to ?-statisticsJournal of Theoretical Probability, Vol. 6, No. 4 Cross Ref On the Accuracy of Normal Approximation of the Probability of Hitting a Ball of Sums of Weakly Dependent Hilbert Space Valued Random Variables IA. N. Tikhomirov17 July 2006 | Theory of Probability & Its Applications, Vol. 36, No. 4AbstractPDF (1136 KB)Normal Approximation in Hilbert Space. IB. A. Zalesskii, V. V. Sazonov, and V. V. Ul’yanov17 July 2006 | Theory of Probability & Its Applications, Vol. 33, No. 2AbstractPDF (1528 KB)Summary of Reports Presented at Sessions of the Seminar on Probability Theory and Mathematical Statistics at the Institute of Mathematics of the Siberian Section of the USSR Academy of Sciences, September–December 19841 August 2006 | Theory of Probability & Its Applications, Vol. 31, No. 1AbstractPDF (545 KB)On the Convergence Rate in the Infinite-Dimensional Central Limit Theorem for Probabilities of Hitting ParallelepipedsA. V. Asriev and V. I. Rotar’28 July 2006 | Theory of Probability & Its Applications, Vol. 30, No. 4AbstractPDF (730 KB)On the Convergence Rate in the Central Limit Theorem on a Class of Sets in Hilbert SpaceB. A. Zalesskii28 July 2006 | Theory of Probability & Its Applications, Vol. 30, No. 4AbstractPDF (703 KB)On the Accuracy of Normal Approximation on Sets Defined by a Smooth Function. IIT. R. Vinogradova17 July 2006 | Theory of Probability & Its Applications, Vol. 30, No. 3AbstractPDF (437 KB)On the Accuracy of Normal Approximation on Sets Defined by a Smooth Function. IT. R. Vinogradova17 July 2006 | Theory of Probability & Its Applications, Vol. 30, No. 2AbstractPDF (1000 KB)Summary of Reports Presented at Sessions of the Probability and Mathematical Statistics Seminar at the Mathematics Institute of the Siberian Section of the USSR Academy of Sciences, February–May 198317 July 2006 | Theory of Probability & Its Applications, Vol. 29, No. 2AbstractPDF (525 KB)Closeness of Moments for Normal Approximation in a Hilbert SpaceB. A. Zalesskii and V. V. Sazonov17 July 2006 | Theory of Probability & Its Applications, Vol. 28, No. 2AbstractPDF (903 KB)Expansions for von Mises functionalsZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 65, No. 4 Cross Ref Bibliography Cross Ref Volume 27, Issue 2| 1983Theory of Probability & Its Applications History Submitted:22 October 1981Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1127031Article page range:pp. 290-298ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics