A Note on Weighted Sums of Associated Random Variables
We prove the convergence of weighted sums of associated random variables normalized by $n^{1/p}$, $p\in(1,2)$, assuming the existence of moments somewhat larger than $p$, depending on the behaviour of the weights, improving on previous results by getting closer to the moment assumption used for the...
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| Format: | article |
| Language: | eng |
| Published: |
2014
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| Online Access: | http://hdl.handle.net/10316/43682 |
| Country: | Portugal |
| Oai: | oai:estudogeral.sib.uc.pt:10316/43682 |
| Summary: | We prove the convergence of weighted sums of associated random variables normalized by $n^{1/p}$, $p\in(1,2)$, assuming the existence of moments somewhat larger than $p$, depending on the behaviour of the weights, improving on previous results by getting closer to the moment assumption used for the case of constant weights. Besides moment conditions we assume a convenient behaviour either on truncated covariances or on joint tail probabilities. Our results extend analogous characterizations known for sums of independent or negatively dependent random variables. |
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