Limit theorems for partial sums of quasi-associated random variables

Abstract

This paper presents a law of the iterated logarithm and a central limit theorem for sums of certain dependent random variables—namely, quasiassociated random variables. Quasiassociation is a form of positive dependence, which is closely related to association and weak association, and it is informative to see how these various modes of association are related. The present interest is in limit theorems for quasiassociated random variables. These results impose slightly stronger restrictions on the covariances of the random variables. Quasiassociation, like association and weak association, is preserved under certain natural actions on the collection of random variables.