dc.contributor.author |
Kuelbs, J |
|
dc.contributor.author |
Meda-Guardiola, Ana |
|
dc.date.accessioned |
2011-01-22T10:26:54Z |
|
dc.date.available |
2011-01-22T10:26:54Z |
|
dc.date.issued |
2002 |
|
dc.identifier.issn |
0304-4149 |
|
dc.identifier.uri |
http://hdl.handle.net/11154/2529 |
|
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 < ε\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 |
|