An Approach to Proving Limit Theorems for Dependent Random Variables

Abstract

Previous article Next article An Approach to Proving Limit Theorems for Dependent Random VariablesB. S. NakhapetyanB. S. Nakhapetyanhttps://doi.org/10.1137/1132080PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. A. Ibragimov and , Yu. V. Linnik, Independent and stationary sequences of random variables, Wolters-Noordhoff Publishing, Groningen, 1971, 443– 48:1287 0219.60027 Google Scholar[2] A. V. Bulinskii, Limit Theorems for Random Processes and Fields, Vol. Moscow, Moscow State University Press, 1981, (In Russian.) Google Scholar[3] Hiroshi Takahata, On the central limit theorem for weakly dependent random fields, Yokohama Math. J., 31 (1983), 67–77 85m:60052 0532.60043 Google Scholar[4] E. Bolthausen, On the central limit theorem for stationary mixing random fields, Ann. Probab., 10 (1982), 1047–1050 84c:60035 0496.60020 CrossrefGoogle Scholar[5] B. S. Nakhapetyan, Central limit theorem for a random field satisfying a strong mixing condition, Dokl. Armen. SSR, 61 (1075), 210–213, (In Russian.) Google Scholar[6] B. S. Nakhapetyan, The central limit theorem for random fields satisfying a strong mixing conditionMulticomponent Random Systems, Nauka, Moscow, 1978, 276–288, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Central limit theorems for stationary random fields under weak dependence with application to ambit and mixed moving average fieldsThe Annals of Applied Probability, Vol. 32, No. 3 | 1 Jun 2022 Cross Ref Compound Poisson approximation for regularly varying fields with application to sequence alignmentBernoulli, Vol. 27, No. 2 | 1 May 2021 Cross Ref Conditional Hazard Estimate for Functional Random FieldsJournal of Statistical Theory and Practice, Vol. 8, No. 2 | 24 March 2014 Cross Ref Robust nonparametric estimation for spatial regressionJournal of Statistical Planning and Inference, Vol. 140, No. 7 | 1 Jul 2010 Cross Ref Asymptotic normality of frequency polygons for random fieldsJournal of Statistical Planning and Inference, Vol. 140, No. 2 | 1 Feb 2010 Cross Ref Estimation of the trend function for spatio-temporal modelsJournal of Nonparametric Statistics, Vol. 21, No. 5 | 1 Jul 2009 Cross Ref Kernel regression estimation for random fieldsJournal of Statistical Planning and Inference, Vol. 137, No. 3 | 1 Mar 2007 Cross Ref LOCAL LINEAR FITTING UNDER NEAR EPOCH DEPENDENCEEconometric Theory, Vol. 23, No. 01 | 6 December 2006 Cross Ref Local linear spatial regressionThe Annals of Statistics, Vol. 32, No. 6 | 1 Dec 2004 Cross Ref Stochastic Dynamics of Fluctuations in Classical Continuous SystemsJournal of Functional Analysis, Vol. 185, No. 1 | 1 Sep 2001 Cross Ref Approximation of Distributions of Sums of Weakly Dependent Random Variables by the Normal DistributionLimit Theorems of Probability Theory | 1 Jan 2000 Cross Ref Kernel density estimation for random fields (density estimation for random fields)Statistics & Probability Letters, Vol. 36, No. 2 | 1 Dec 1997 Cross Ref Kernel density estimation for random fields: The L1 TheoryJournal of Nonparametric Statistics, Vol. 6, No. 2-3 | 1 Jan 1996 Cross Ref Kernel density estimation on random fieldsJournal of Multivariate Analysis, Vol. 34, No. 1 | 1 Jul 1990 Cross Ref Volume 32, Issue 3| 1988Theory of Probability & Its Applications389-571 History Submitted:01 April 1986Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1132080Article page range:pp. 535-539ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics