Some Limit Theorems for Polynomials of Second Degree

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Previous article Next article Some Limit Theorems for Polynomials of Second DegreeV. I. Rotar'V. I. Rotar'https://doi.org/10.1137/1118064PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] B. A. Sevast'yanov, A class of limit distributions for quadratic forms of stochastic random variables, Theory Prob. Applications, 6 (1961), 337–340 0286.60028 Google Scholar[2] Arthur Grad and , Herbert Solomon, Distribution of quadratic forms and some applications, Ann. Math. Statist., 26 (1955), 464–477 MR0074704 (17,634e) 0066.38301 CrossrefGoogle Scholar[3] John Gurland, Distribution of definite and of indefinite quadratic forms, Ann. Math. Statist., 26 (1955), 122–127 MR0067417 (16,727b) 0064.12902 CrossrefGoogle Scholar[4] Samuel Kotz, , N. L. Johnson and , D. W. Boyd, Series representations of distributions of quadratic forms in normal variables. I. Central case, Ann. Math. 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Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963xvi+685 MR0203748 (34:3596) 0108.14202 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails LIMIT THEOREMS FOR FACTOR MODELS9 November 2020 | Econometric Theory, Vol. 37, No. 5 Cross Ref A bound on the Wasserstein-2 distance between linear combinations of independent random variablesStochastic Processes and their Applications, Vol. 129, No. 7 Cross Ref Thresholds for detecting an anomalous path from noisy environmentsThe Annals of Applied Probability, Vol. 28, No. 5 Cross Ref Asymptotic normality of quadratic forms with random vectors of increasing dimensionJournal of Multivariate Analysis, Vol. 164 Cross Ref Universal limit theorems in graph coloring problems with connections to extremal combinatoricsThe Annals of Applied Probability, Vol. 27, No. 1 Cross Ref Modeling and testing for joint association using a genetic random field model13 March 2014 | Biometrics, Vol. 70, No. 3 Cross Ref Improved GMM estimation of random effects panel data models with spatially correlated error components27 February 2013 | Papers in Regional Science, Vol. 93, No. 1 Cross Ref Stein's method in high dimensions with applicationsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 49, No. 2 Cross Ref A new method of normal approximationThe Annals of Probability, Vol. 36, No. 4 Cross Ref Asymptotic Expansions in Non-central Limit Theorems for Quadratic FormsJournal of Theoretical Probability, Vol. 18, No. 4 Cross Ref On a Functional Version of the Convergence of a Quadratic Form in Independent Martingalesto a $\chi^2$ DistributionB. 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Rotar'17 July 2006 | Theory of Probability & Its Applications, Vol. 20, No. 3AbstractPDF (1495 KB) Volume 18, Issue 3| 1974Theory of Probability & Its Applications History Submitted:25 November 1971Published online:28 July 2006 InformationCopyright © 1974 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1118064Article page range:pp. 499-507ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics