Bounds for Characteristic Functions of Certain Degenerate Multidimensional Distributions

Previous article Next article Bounds for Characteristic Functions of Certain Degenerate Multidimensional DistributionsV. V. JurinskiiV. V. Jurinskiihttps://doi.org/10.1137/1117008PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] S. M. Sadikova, Some inequalities for characteristic functions, Theory Prob. Applications, 11 (1966), 441–447 10.1137/1111044 LinkGoogle Scholar[2] J. G. van der Corput, Zahlentheoretische Abschätzungen, Math. Ann., 84 (1921), 53–79 10.1007/BF01458693 MR1512020 CrossrefGoogle Scholar[3] Joachim Focke, Asymptotische Entwicklungen mittels der Methode der stationären Phase, Ber. Verh. Sächs. Akad. Wiss. Leipzig. Math.-Nat. Kl., 101 (1954), 48– MR0068650 0057.04901 Google Scholar[4] M. V. Fedoryuk, The stationary phase method for multiple integrals, Z. Vyčisl. Mat. i Mat. Fiz., 2 (1962), 145–150, (In Russian.) MR0146579 0122.12401 Google Scholar[5] M. V. Fedoryuk, The stationary-phase method. Near-by saddle points in the higher-dimensional case, Ž. Vyčisl. Mat. i Mat. Fiz., 4 (1964), 671–682, (In Russian.) MR0166533 0173.15003 Google Scholar[6] Naum I. Akhiezer, The calculus of variations, Translated from the Russian by Aline H. Frink. A Blaisdell Book in the pure and Applied Sciences, Blaisdell Publishing Co. (A Division of Random House, Inc.), New York-London, 1962viii+248 MR0142019 Google Scholar[7] B. V. Shabat, Introduction to Complex Analysis, Nauka, Moscow, 1969, (In Russian.) Google Scholar[8] Yu. V. Prokhorov, Local theorems for densities, DAN SSSR 83, 6 (1952), 797–800, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Explicit parametrix and local limit theorems for some degenerate diffusion processesAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 46, No. 4 | 1 Nov 2010 Cross Ref Asymptotic expansions in the integral and local limit theorems in banach spaces with applications to ?-statisticsJournal of Theoretical Probability, Vol. 6, No. 4 | 1 Oct 1993 Cross Ref Borel Normal Vectors on a Manifold in RⁿTheory of Probability & Its Applications, Vol. 36, No. 2 | 17 July 2006AbstractPDF (449 KB)Generalizations of Khinchin’s inequalityTheory of Probability & Its Applications, Vol. 35, No. 4 | 17 July 2006AbstractPDF (690 KB)On the edgeworth expansion for the sum of a function of uniform spacingsJournal of Statistical Planning and Inference, Vol. 17 | 1 Jan 1987 Cross Ref Estimates of Characteristic Functions of Certain Random Variables with Application to ω ²-Statistics. ITheory of Probability & Its Applications, Vol. 29, No. 3 | 17 July 2006AbstractPDF (1126 KB)Asymptotic Expansions in Parametric Statistical TheoryDevelopments in Statistics | 1 Jan 1980 Cross Ref Summary of Papers Presented at Sessions of the Probability and Statistics Section of the Moscow Mathematical Society (February–October 1974)Theory of Probability & Its Applications, Vol. 20, No. 2 | 17 July 2006AbstractPDF (1740 KB)An Asymptotic Expansion for the Distribution of a Statistic Admitting an Asymptotic ExpansionTheory of Probability & Its Applications, Vol. 17, No. 4 | 28 July 2006AbstractPDF (880 KB) Volume 17, Issue 1| 1972Theory of Probability & Its Applications1-198 History Submitted:07 July 1970Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1117008Article page range:pp. 101-113ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics