ABSTRACT

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.

中文翻译：

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m-ANA 随机变量和统计应用的完整矩收敛

摘要

在本文中，基于慢变函数的性质和 de Bruijn 共轭，我们建立了m渐近负相关随机变量的随机加权和的完全矩收敛的一般结果。这些结果应用于具有随机设计的 bootstrap 样本均值和非参数回归模型。给出了模拟研究随机设计和引导样本均值的非参数回归模型中最近邻权重函数估计器一致性的数值性能。