Almost sure convergence for weighted sums of pairwise PQD random variables

Abstract

We obtain Marcinkiewicz-Zygmund strong laws of large numbers for weighted sums of pairwise positively quadrant dependent random variables stochastically dominated by a random variable $X\in {\mathcal{L}}_p$, $1⩽p<2$. We use our results to establish the strong consistency of estimators which emerge from regression models having pairwise positively quadrant dependent errors.

23 pages