On Limit Distributions of Random Symmetric Polynomials
L. Seidl’ · Theory of Probability and Its Applications · 1989
Previous article Next article On Limit Distributions of Random Symmetric PolynomialsL. Seidl’L. Seidl’https://doi.org/10.1137/1133040PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. von Mises, On the asymptotic distribution of differentiable statistical functions, Ann. Math. Statistics, 18 (1947), 309–348 9,194h 0037.08401 CrossrefGoogle Scholar[2] Wassily Hoeffding, A class of statistics with asymptotically normal distribution, Ann. Math. Statisitcs, 19 (1948), 293–325 10,134g 0032.04101 CrossrefGoogle Scholar[3] Robert J. Serfling, Approximation theorems of mathematical statistics, John Wiley & Sons Inc., New York, 1980xiv+371 82a:62003 0538.62002 CrossrefGoogle Scholar[4] V. S. Korolyuk and , Yu. Z. Borovskikh, The Asymptotic Analysis of Statistical Distributions, Naukoya Dumka, Kiev, 1984, (In Russian.) Google Scholar[5] H. Rubin and , R. A. Vitale, Asymptotic distribution of symmetric statistics, Ann. Statist., 8 (1980), 165–170 81a:62018 0422.62016 CrossrefGoogle Scholar[6] E. B. Dynkin and , A. Mandelbaum, Symmetric statistics, Poisson point processes, and multiple Wiener integrals, Ann. Statist., 11 (1983), 739–745 85b:60015 0518.60050 CrossrefGoogle Scholar[7] G Halász and , G. J. Székely, On the elementary symmetric polynomials of independent random variables, Acta Math. Acad. Sci. Hungar., 28 (1976), 397–400 54:11467 0349.60053 CrossrefGoogle Scholar[8] T. F. Mort, On a Hoeffding-type problemThe First Pannonian Symposium on Mathematical Statistics (Bad Tatzmannsdorf, 1979), Lecture Notes in Statist., Vol. 8, Springer, New York, 1981, 174–181, Berlin 82h:60045 CrossrefGoogle Scholar[9] T. F. Mort and , G. J. Szekely, Asymptotic behaviour of symmetric polynomial statistics, Ann. Probab., 10 (1982), 124–131 83a:60042 CrossrefGoogle Scholar[10] G. F. Szekely, A limit theorem for elementary symmetric polynomials of independent random variables, Z. Wahrsch. Verw. Gebiete, 59 (1982), 355–359 85a:60030 0468.60029 CrossrefGoogle Scholar[11] V. M. Zolotarev, Limit theorems for random symmetric polynomials, Theory Probab. Appl., 30 (1985), 636–637 Google Scholar[12] V. M. Zolotarev, The limit distribution of Student's statistic for a non-Gaussian population, Stability Problems of Stochastic Models, Proceedings of the Seminar, VNIISI, Moscow, 1985, 57–63, (In Russian.) Google Scholar[13] V. M. Zolotarev, On random symmetric polynomialsProbability Distributions and Mathematical Statistics, Fan, Tashkent, 1980, 170–188, (In Russian.) Google Scholar[14] L. Seidl', On the limit distributions of random symmetric functions, Theory Probab. Appl., 31 (1986), 590–603 10.1137/1131083 LinkGoogle Scholar[15] L. L. Branitskaya, On limit distributions of third-degree random symmetric polynomials, Theory Probab. Appl., 31 (1986), 715–717 10.1137/1131099 0664.60029 LinkGoogle Scholar[16] Florin Avram and , Murad S. Taqqu, Symmetric polynomials of random variables attracted to an infinitely divisible law, Probab. Theory Relat. Fields, 71 (1986), 491–500 87h:60047 0579.60021 CrossrefGoogle Scholar[17] A. P. Prudnikov, , Yu. A. Brychkov and , O. I. Marichev, Integrals and Series, Nauka, Moscow, 1981, (In Russian.) 0511.00044 Google Scholar[18] T. L. Malevich and , B. Abdalimov, Stable limit distributions for U-statistics, Theory Probab. Appl., 22 (1977), 370–377 10.1137/1122041 0387.60028 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails О числе единиц в выходной последовательности обобщенного генератора ПолаДискретная математика, Vol. 31, No. 1 | 1 Jan 2019 Cross Ref On the Characteristic Function of the Joint Limit Distribution of the First- and Second-Order Power SumsGy. Michaletzky, L. Szeidl, and P. VarlakiTheory of Probability & Its Applications, Vol. 43, No. 1 | 25 July 2006AbstractPDF (270 KB)On the Limit Distributions of Homogeneous Random Symmetric Polynomials of Arbitrary DegreeO. L. YanushkevichieneTheory of Probability & Its Applications, Vol. 40, No. 3 | 12 July 2006AbstractPDF (627 KB)Weak invariance principles for weightedU-statisticsJournal of Theoretical Probability, Vol. 7, No. 1 | 1 Jan 1994 Cross Ref Analytic Description of Limit Laws for Sequences of Random Symmetric PolynomialsL. Seidl’Theory of Probability & Its Applications, Vol. 35, No. 1 | 17 July 2006AbstractPDF (361 KB)The Quantile-Transform-Empirical-Process Approach to Limit Theorems for Sums of Order StatisticsSums, Trimmed Sums and Extremes | 1 Jan 1991 Cross Ref Volume 33, Issue 2| 1989Theory of Probability & Its Applications207-404 History Submitted:08 October 1987Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1133040Article page range:pp. 248-259ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics