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 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.