On the Limit Distributions of Random Symmetric Functions
L. Seidl’ · Theory of Probability and Its Applications · 1987
Previous article Next article On the Limit Distributions of Random Symmetric FunctionsL. Seidl’L. Seidl’https://doi.org/10.1137/1131083PDFBibTexSections 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 1001.62005 CrossrefGoogle Scholar[4] V. S. Korolyuk and , Yu. V. Borovskikh, Asymptotic Analysis of the Distribution of a Statistic, Naukova 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] T. Mori, 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 82h:60045 0476.62024 CrossrefGoogle Scholar[8] V. M. Zolotarev, Limit theorems for random symmetric polynomials, Theory Probab. Appl., 30 (1985), 636–637 Google Scholar[9] H. Cramér, Mathematical Methods of Statistics, Princeton University Press, Princeton, NJ, 1957 Google Scholar[10] B. F. Logan, , C. L. Mallows, , S. O. Rice and , L. A. Shepp, Limit distributions of self-normalized sums, Ann. Probability, 1 (1973), 788–809 50:14890 0272.60016 CrossrefGoogle Scholar[11] K. Schmidt, Stable probability measures on ${\rm R} u$, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 33 (1975/76), 19–31 54:3804 0347.60015 CrossrefGoogle Scholar[12] E. Lukacs, Characteristic Functions, Hefner, London, 1972 Google Scholar[13] A. A. Borovkov, Probability Theory, Nauka, Moscow, 1976, (In Russian.) 0463.60001 Google Scholar[14] V. N. Zolotarev, Random symmetric polynomialsProbability distributions and mathematical statistics (Russian) (Fergana, 1983), “Fan”, Tashkent, 1986, 170–188, 492 89c:60031 Google Scholar[15] V. N. Zolotarev, Limit distribution of Student's statistic in the case of the non-Gaussian parent population in Problems on the Stability of Stochastic Models, Proc. Seminar, VNIICI, Moscow, 1985, 57–63, (In Russian.) Google Scholar[16] B. A. Sevast'yanov, A class of limit distributions for quadratic forms of normal stochastic variables, Theory Probab. Appl., 6 (1961), 337–340 0286.60028 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Limit Laws for Symmetric k-Tensors of Regularly Varying MeasuresJournal of Multivariate Analysis, Vol. 73, No. 2 | 1 May 2000 Cross Ref Limit theorems for random symmetric functionsJournal of Mathematical Sciences, Vol. 89, No. 5 | 1 May 1998 Cross Ref Weak invariance principles for weightedU-statisticsJournal of Theoretical Probability, Vol. 7, No. 1 | 1 Jan 1994 Cross Ref Korean Journal of Computational & Applied Mathematics, Vol. 1, No. 1 | 1994 Cross Ref The Suzdal International Seminar of 1991 on Stability Problems for Stochastic ModelsTheory of Probability & Its Applications, Vol. 36, No. 4 | 17 July 2006AbstractPDF (5581 KB)Analytic Description of Limit Laws for Sequences of Random Symmetric PolynomialsTheory of Probability & Its Applications, Vol. 35, No. 1 | 17 July 2006AbstractPDF (361 KB)On Limit Distributions of Random Symmetric PolynomialsTheory of Probability & Its Applications, Vol. 33, No. 2 | 17 July 2006AbstractPDF (1083 KB)On Limit Distributions of Third-Degree Random Symmetric PolynomialsTheory of Probability & Its Applications, Vol. 31, No. 4 | 17 July 2006AbstractPDF (321 KB) Volume 31, Issue 4| 1987Theory of Probability & Its Applications563-742 History Submitted:12 June 1986Published online:17 July 2006 InformationCopyright © 1987 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1131083Article page range:pp. 590-603ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics