On Inequalities for Large Deviations for Certain Statistics

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Previous article Next article On Inequalities for Large Deviations for Certain StatisticsV. V. YurinskiiV. V. Yurinskiihttps://doi.org/10.1137/1116039PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. M. Dudley, Weak convergences of probabilities on nonseperable metric spaces and empirical measures on Euclidean spaces, Illinois J. Math., 10 (1966), 109–126 MR0185641 CrossrefGoogle Scholar[2] J. Kiefer, On large deviations of the empiric D. F. of vector chance variables and a law of the iterated logarithm, Pacific J. Math., 11 (1961), 649–660 MR0131885 0119.34904 CrossrefGoogle Scholar[3] V. V. Yurinskii, On an infinite-dimensional version of S. N. Bernshtein's inequalities, Theory Prob. Applications, 15 (1970), 108–109 10.1137/1115008 0216.46601 LinkGoogle Scholar[4] Wassily Hoeffding, Probability inequalities for sums of bounded random variables, J. Amer. Statist. Assoc., 58 (1963), 13–30 MR0144363 0127.10602 CrossrefGoogle Scholar[5] A. V. Prokhorov, Masters Thesis, Inequalities for sums of independent multi-dimensional random variables, Cand. Dist., Moscow, 1968, (In Russian.) Google Scholar[6] I. N. Sanov, On the probability of large deviations of random magnitudes, Mat. Sb. N. S., 42 (84) (1957), 11–44, (In Russian.) MR0088087 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails A Nonasymptotic Bound for Deviation of a Multidimensional Empirical Distribution FunctionE. I. Gaivoronskii and E I. Ostrovskii17 July 2006 | Theory of Probability & Its Applications, Vol. 36, No. 3AbstractPDF (269 KB)An inequality for differences of distribution functionsArchiv der Mathematik, Vol. 54, No. 2 Cross Ref On some inequalities in the theory of uniform distribution, IProceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 64, No. 3 Cross Ref On Large Deviation Probabilities for Sums of Independent Random VectorsL. V. Osipov17 July 2006 | Theory of Probability & Its Applications, Vol. 23, No. 3AbstractPDF (1498 KB)Summary of Papers Presented at Sessions of the Probability and Statistics Section of the Moscow Mathematical Society (February–October 1974)17 July 2006 | Theory of Probability & Its Applications, Vol. 20, No. 2AbstractPDF (1740 KB) Volume 16, Issue 2| 1971Theory of Probability & Its Applications History Submitted:15 January 1971Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1116039Article page range:pp. 385-387ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics