Estimates of the Moments of Sums of Independent Random Variables

Previous article Next article Estimates of the Moments of Sums of Independent Random VariablesI. F. Pinelis and S. A. UtevI. F. Pinelis and S. A. Utevhttps://doi.org/10.1137/1129075PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Haskell P. Rosenthal, On the subspaces of $L\sp{p}$$(p>2)$ spanned by sequences of independent random variables, Israel J. Math., 8 (1970), 273–303 42:6602 0213.19303 CrossrefGoogle Scholar[2] Haskell P. Rosenthal, On the span in Lp of sequences of independent random variables. II, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. II: Probability theory, Univ. California Press, Berkeley, Calif., 1972, 149–167 55:13229 0255.60003 Google Scholar[3] V. V. Sazonov, On the estimation of moments of sums of independent random variables, Theory Prob. Appl., 19 (1974), 371–374 LinkGoogle Scholar[4] S. V. Nagaev and , I. F. Pinelis, Some inequalities for the distributions of sums of independent random variables, Theory Prob. Appl., 22 (1977), 248–256 LinkGoogle Scholar[5] I. F. Pinelis, Estimates of moments of infinite-dimensional martingales, Math. Notes, 27 (1980), 459–462 0461.60062 CrossrefGoogle Scholar[6] Yu. V. Prokhorov, Extremum problems in limit theorems, Proc. VI All-Union Conference on Probability Theory and Statistics, Vil'nyus, 1962, 77–84, (In Russian.) Google Scholar[7] Patrick Billingsley, Convergence of probability measures, John Wiley & Sons Inc., New York, 1968xii+253 38:1718 0172.21201 Google Scholar[8] V. P. Leonov and , A. N. Shiryaev, On a method of calculation of cumulants, Theor. Probability Appl., 4 (1959), 319–329 LinkGoogle Scholar[9] S. W. Dharmadhikari and , Kumar Jogdeo, Bounds on moments of certain random variables, Ann. Math. Statist., 40 (1969), 1506–1509 39:4908 0208.44903 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Fooling PolytopesJournal of the ACM, Vol. 69, No. 2 | 30 Apr 2022 Cross Ref Exact Rosenthal-type boundsThe Annals of Probability, Vol. 43, No. 5 | 1 Sep 2015 Cross Ref Rosenthal-Type Inequalities for Martingales in 2-Smooth Banach SpacesI. PinelisTheory of Probability & Its Applications, Vol. 59, No. 4 | 19 November 2015AbstractPDF (160 KB)A note on moment inequality for quadratic formsStatistics & Probability Letters, Vol. 92 | 1 Sep 2014 Cross Ref Berry–Esseen bounds in the entropic central limit theoremProbability Theory and Related Fields, Vol. 159, No. 3-4 | 12 June 2013 Cross Ref Exact Rosenthal-type inequalities for , and related resultsStatistics & Probability Letters, Vol. 83, No. 12 | 1 Dec 2013 Cross Ref Noncommutative Bennett and Rosenthal inequalitiesThe Annals of Probability, Vol. 41, No. 6 | 1 Nov 2013 Cross Ref Optimal constants in the Rosenthal inequality for random variables with zero odd momentsStatistics & Probability Letters, Vol. 78, No. 2 | 1 Feb 2008 Cross Ref On extremal distributions and sharp $\bolds{L_p}$-bounds\\ for sums of multilinear formsThe Annals of Probability, Vol. 31, No. 2 | 1 Apr 2003 Cross Ref The Exact Constant in the Rosenthal Inequality for Random Variables with Mean ZeroR. Ibragimov and Sh. SharakhmetovTheory of Probability & Its Applications, Vol. 46, No. 1 | 25 July 2006AbstractPDF (111 KB)The best constant in the Rosenthal inequality for nonnegative random variablesStatistics & Probability Letters, Vol. 55, No. 4 | 1 Dec 2001 Cross Ref Short Communications: On an Exact Constant for the Rosenthal InequalityR. Ibragimov and Sh. SharakhmetovTheory of Probability & Its Applications, Vol. 42, No. 2 | 17 February 2012AbstractPDF (234 KB)An Approach to Inequalities for the Distributions of Infinite-Dimensional MartingalesProbability in Banach Spaces, 8: | 1 Jan 1992 Cross Ref Exact Exponential Bounds for Sums of Independent Random VariablesI. S. Pinelis and S. A. UtevTheory of Probability & Its Applications, Vol. 34, No. 2 | 17 July 2006AbstractPDF (616 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 1984Theory of Probability & Its Applications, Vol. 31, No. 1 | 1 August 2006AbstractPDF (545 KB) Volume 29, Issue 3| 1985Theory of Probability & Its Applications427-645 History Submitted:06 May 1982Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1129075Article page range:pp. 574-577ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

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