Strong laws of large numbers for arrays of row-wise extended negatively dependent random variables with applications

Abstract

ABSTRACTThe main purpose of this paper is to obtain strong laws of large numbers for arrays or weighted sums of random variables under a scenario of dependence. Namely, for triangular arrays of row-wise extended negatively dependent random variables weakly mean dominated by a random variable and sequences of positive constants, conditions are given to ensure . Our statements allow us to establish strong consistency of general nonparametric estimates in a nonparametric regression model having fixed design points.