Previous article Next article Convergence Rate of the Dependent Bootstrapped MeansA. Volodin, M. Ordóñez Cabrera, and T. C. HuA. Volodin, M. Ordóñez Cabrera, and T. C. Huhttps://doi.org/10.1137/S0040585X97981688PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractIn this paper, a Baum--Katz, Erdös, Hsu--Robbins, Spitzer type complete convergence result is obtained for the dependent bootstrapped means.[1] Eusebio Arenal‐Gutiérrez, , Carlos Matrán and , Juan Cuesta‐Albertos, On the unconditional strong law of large numbers for the bootstrap mean, Statist. Probab. Lett., 27 (1996), 49–60 97h:60020 CrossrefGoogle Scholar[2] K. Athreya, Strong law for the bootstrap, Statist. Probab. Lett., 1 (1983), 147–150 84g:62026 CrossrefGoogle Scholar[3] G. R. Barnes and and H. G. Tucker, On almost sure convergence of normed maxima of independent random variables, J. London Math. Soc. (2), 16 (1977), pp. 377–383. axi JLMSAK 0024-6107 J. Lond. Math. Soc. CrossrefGoogle Scholar[4] Peter Bickel and , David Freedman, Some asymptotic theory for the bootstrap, Ann. Statist., 9 (1981), 1196–1217 83a:62051 CrossrefGoogle Scholar[5] Google Scholar[6] Sándor Csörgö, On the law of large numbers for the bootstrap mean, Statist. Probab. Lett., 14 (1992), 1–7 93g:60063 CrossrefGoogle Scholar[7] B. Efron, Bootstrap methods: Another look at the jackknife, Ann Statist., 7 (1979), pp. 1–26. 9j7 ASTSC7 0090-5364 Ann. Stat. CrossrefGoogle Scholar[8] E. L. Lehmann, Some concepts of dependence, Ann. Math. Statist., 37 (1966), pp. 1137–1153. aax AASTAD 0003-4851 Ann. Math. Stat. CrossrefGoogle Scholar[9] Deli Li, , Andrew Rosalsky and , S. Ahmed, Complete convergence of bootstrapped means and moments of the supremum of normed bootstrapped sums, Stochastic Anal. Appl., 17 (1999), 799–814 2001g:60067 CrossrefGoogle Scholar[10] T. Mikosch, Almost sure convergence of bootstrapped means and U‐statistics, J. Statist. Plann. Inference, 41 (1994), 1–19 95h:60046 CrossrefGoogle Scholar[11] Valentin Petrov, On the strong law of large numbers, Statist. Probab. Lett., 26 (1996), 377–380 97d:60063 CrossrefGoogle Scholar[12] W. Smith and and R. L. Taylor, Consistency of dependent bootstrap estimators, Amer. J. Math. Management Sci., 21 (2001), pp. 359–382. a2a ZZZZZZ 0196-6324 Am. J. Math. Manage. Sci. Google Scholar[13] Google ScholarKeywordsbootstrapped meansdependent bootstraprate of convergenceexponential inequalitiesstrong law of large numbers Previous article Next article FiguresRelatedReferencesCited byDetails Complete moment convergence of weighted sums for arrays of negatively dependent random variables and its applications3 September 2015 | Communications in Statistics - Theory and Methods, Vol. 45, No. 11 Cross Ref Complete convergence theorems for normed row sums from an array of rowwise pairwise negative quadrant dependent random variables with application to the dependent bootstrap13 September 2015 | Applications of Mathematics, Vol. 60, No. 3 Cross Ref Limiting behaviour for arrays of row-wise END random variables under conditions of h -integrability29 October 2014 | Stochastics, Vol. 87, No. 3 Cross Ref On limiting behavior for arrays of rowwise negatively orthant dependent random variablesJournal of the Korean Statistical Society, Vol. 42, No. 1 Cross Ref Equivalent Conditions of Complete Convergence for Weighted Sums of Sequences of Negatively Dependent Random VariablesAbstract and Applied Analysis, Vol. 2012 Cross Ref Convergence properties of partial sums for arrays of rowwise negatively orthant dependent random variablesJournal of the Korean Statistical Society, Vol. 39, No. 2 Cross Ref Volume 50, Issue 2| 2006Theory of Probability & Its Applications History Published online:25 July 2006 InformationCopyright © 2006 Society for Industrial and Applied MathematicsKeywordsbootstrapped meansdependent bootstraprate of convergenceexponential inequalitiesstrong law of large numbersPDF Download Article & Publication DataArticle DOI:10.1137/S0040585X97981688Article page range:pp. 337-346ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics