Complete moment convergence for m-ANA random variables and statistical applications

In this paper, based on the properties of slowly varying functions and the de Bruijn conjugates, we establish general results on complete moment convergence for randomly weighted sums of m-asymptotic negatively associated random variables. These results are applied to the bootstrap sample means and nonparametric regression models with random design. Simulations to study the numerical performance of the consistency for the nearest neighbour weight function estimator in non parametric regression model with random design and bootstrap sample means are given.