Weighted sums of associated variables

We study the convergence of weighted sums of associated random variables. The convergence for the typical $n^{1/p}$ normalization is proved assuming finiteness of moments somewhat larger than p, but still smaller than 2, together with suitable control on the covariance structure described by a trunc...

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Bibliographic Details
Published inJournal of the Korean Statistical Society Vol. 41; no. 4; pp. 537 - 542
Main Author Oliveira, Paulo Eduardo
Format Journal Article
LanguageKorean
Published 2012
Subjects
Association
Almost sure convergence
Weighted sums
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Summary:We study the convergence of weighted sums of associated random variables. The convergence for the typical $n^{1/p}$ normalization is proved assuming finiteness of moments somewhat larger than p, but still smaller than 2, together with suitable control on the covariance structure described by a truncation that generates covariances that do not grow too quickly. We also consider normalizations of the form $n^{1/p}log^{1/{\gamma}}n$, where q is now linked with the properties of the weighting sequence. We prove the convergence under a moment assumption than is weaker that the usual existence of the moment-generating function. Our results extend analogous characterizations known for sums of independent or negatively dependent random variables.
Bibliography:KISTI1.1003/JNL.JAKO201214350262901
ISSN:1226-3192