Rates of convergence for the Nummelin conditional weak law of large numbers

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Show simple item record Kuelbs, J Meda-Guardiola, Ana 2011-01-22T10:26:54Z 2011-01-22T10:26:54Z 2002
dc.identifier.issn 0304-4149
dc.description.abstract Let (B, parallel to . parallel to) be a real separable Banach space of dimension 1 less than or equal to d less than or equal to infinity, and assume X,X-1, X-2,... are i.i.d. B valued random vectors with law mu=L(X) and mean m=integral(B) xdmu(x). Nummelin's conditional weak law of large numbers establishes that under suitable conditions on (D subset of B, mu) and for every epsilon > 0, lim(n) P(parallel toS(n)/n-a(0)parallel to < &epsilon;\S-n/n &ISIN en_US
dc.description.abstract D)=1, with a(0) the dominating point of D and S-n = &USigma;(n)(j=1) X-j. We study the rates of convergence of such laws, i.e., we examine lim(n) P(parallel toS(n)/n - a(0)parallel to < t/n(r)/S-n/n &ISIN en_US
dc.description.abstract D) as d, r, t and D vary. It turns out that the limit is sensitive to variations in these parameters. Additionally, we supply another proof of Nummelin's law of large numbers. Our results are most complete when 1 &LE en_US
dc.description.abstract d < infinity, but we also include results when d=infinity, mainly in Hilbert space. A connection to the Gibbs conditioning principle is also examined. (C) 2001 Elsevier Science B.V. All rights reserved. en_US
dc.language.iso en en_US
dc.title Rates of convergence for the Nummelin conditional weak law of large numbers en_US
dc.type Article en_US
dc.identifier.idprometeo 2231
dc.source.novolpages 98(2):229-252
dc.subject.wos Statistics & Probability
dc.description.index WoS: SCI, SSCI o AHCI
dc.subject.keywords large deviation probabilities
dc.subject.keywords dominating points
dc.subject.keywords Nummelin's conditional law of large numbers
dc.subject.keywords rates of convergence
dc.subject.keywords conditional limit theorems
dc.subject.keywords Gibbs conditioning principle
dc.relation.journal Stochastic Processes and their Applications

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