On the invariance principle for empirical processes of associated sequences

TL;DR

This paper extends the invariance principle for empirical processes of associated sequences by relaxing covariance decay conditions under certain distributional assumptions, broadening applicability.

Contribution

It introduces new conditions on pairwise distributions that allow for slower covariance decay while maintaining the invariance principle.

Findings

Invariance principle holds under relaxed covariance decay conditions.

Certain distributional assumptions enable broader applicability.

Results extend previous work by Louhichi on associated sequences.

Abstract

We consider empirical processes generated by strictly stationary sequences of associated random variables. S. Louhichi established an invariance principle for such processes, assuming that the covariance function decays rapidly enough. We show that under certain conditions imposed on the pairwise distributions of the random variables in question the restrictions on the rate of decay of the covariance function can be relaxed.