Approximation of Nondegenerate U -Statistics
Volodymyr S. Korolyuk, Yu. V. Borovskikh · Theory of Probability and Its Applications · 1986
Next article Approximation of Nondegenerate U-StatisticsV. S. Korolyuk and Yu. V. BorovskikhV. S. Korolyuk and Yu. V. Borovskikhhttps://doi.org/10.1137/1130057PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Yu. V. Borovskikh, The Problem of Approximating the Distributions of U-Statistics and Mises' Functionals, 1, 1980, Preprint Inst. Mathematics of the Ukrain. SSR Acad. of Sciences 80.6, Kiev, (In Russian.) Google Scholar[2] Yu. V. Borovskikh, The Problem of Approximating the Distributions of U-Statistics and Mises' Functionals, II, 1980, Preprint Inst. Mathematics of the Ukrain. SSR Acad. of Sciences, 80.7, Kiev, (In Russian.) Google Scholar[3] T. L. Malevich and , B. A. Abdalimov, Estimation of the deviation of the distribution of a U-statistic from the normal distribution, Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk, (1979), 10–13, 92, (In Russian.) 80i:60023 0422.62018 Google Scholar[4] Herman Callaert and , Paul Janssen, The Berry-Esseen theorem for U-statistics, Ann. Statist., 6 (1978), 417–421 57:4290 0393.60022 CrossrefGoogle Scholar[5] Y.-K. Chan and , John Wierman, On the Berry-Esseen theorem for U-statistics, Ann. Probability, 5 (1977), 136–139 55:6527 0381.60022 CrossrefGoogle Scholar[6] R. Helmers and , W. R. van Zwet, S. S. Gupta and , J. O. Berger, The Berry-Esseen bound for U-statisticsStatistical decision theory and related topics, III, Vol. 1 (West Lafayette, Ind., 1981), Academic Press, New York, 1982, 497–512 85c:60027 0598.62016 Google Scholar[7] S. D. Chatterji, An $L\sp{p}$-convergence theorem, Ann. Math. Statist., 40 (1969), 1068–1070 40:4996 0176.48101 CrossrefGoogle Scholar[8] Bengt von Bahr and , C. G. Esseen, Inequalities for the rth absolute moment of a sum of random variables, $1\leq r\leq 2$, Ann. Math. Statist, 36 (1965), 299–303 30:645 0134.36902 CrossrefGoogle Scholar[9] Bengt von Bahr, On the convergence of moments in the central limit theorem, Ann. Math. Statist., 36 (1965), 808–818 31:4068 0139.35301 CrossrefGoogle Scholar[10] T. L. Malevich and , B. A. Abdalimov, Stable limit distributions of U-statistics, Theory Prob. Appl., 22 (1977), 370–377 0387.60028 LinkGoogle Scholar[11] A. D. Slastnikov, Limit theorems for moderate deviation probabilities, Theory Prob. Appl., 23 (1978), 322–340 0452.60041 LinkGoogle Scholar[12] A. F. Ronzhin, Asymptotic formulas for the moments of U-statistics with degenerate kernel, Theory Prob. Appl., 27 (1982), 49–58 LinkGoogle Scholar[13] N. Bönner and , H. P. Kirschner, Note on conditions for weak convergence of von Mises' differentiable statistical functions, Ann. Statist., 5 (1977), 405–407 55:1566 0358.62018 CrossrefGoogle Scholar Next article FiguresRelatedReferencesCited byDetails On normal approximations to U-statisticsThe Annals of Probability, Vol. 37, No. 6 Cross Ref Lyapunov-Type Bounds for U-StatisticsI. B. Alberlink and V. Bentkus25 July 2006 | Theory of Probability & Its Applications, Vol. 46, No. 4AbstractPDF (202 KB)On a Normal Approximation of U-StatisticsYu. V. Borovskikh25 July 2006 | Theory of Probability & Its Applications, Vol. 45, No. 3AbstractPDF (211 KB)Normal Approximation of U-Statistics in Hilbert SpaceYu. V. Borovskikh, L. Madan Puri, and V. V. Sazonov25 July 2006 | Theory of Probability & Its Applications, Vol. 41, No. 3AbstractPDF (598 KB)Some asymptotic results for a broad class of nonparametric statisticsJournal of Statistical Planning and Inference, Vol. 32, No. 2 Cross Ref Improved Berry-Esseen-Chebyshev Bounds with Statisical Applications18 October 2010 | Econometric Theory, Vol. 8, No. 2 Cross Ref Volume 30, Issue 3| 1986Theory of Probability & Its Applications History Submitted:23 July 1984Published online:17 July 2006 InformationCopyright © 1986 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1130057Article page range:pp. 439-450ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics