In this paper, we investigate the complete convergence for weighted sums of widely orthant-dependent (WOD, for short) random variables. Our results extend the corresponding ones of Chen and Sung (Stat Probab Lett 154, 2019) to a much more general type of complete convergence. As an application of our main results, we establish the complete consistency for the estimator in the nonparametric regression models and provide a simulation study to assess the finite sample performance of the theoretical results.

中文翻译：

---

广义正态相关随机变量加权和的完全收敛及其统计应用

在本文中，我们研究了广泛依赖于Orthant的随机变量（简称WOD）的加权和的完全收敛性。我们的结果将Chen和Sung（Stat Probab Lett 154，2019）的相应研究扩展到了一种更通用的完全收敛类型。作为我们主要结果的应用，我们在非参数回归模型中建立了估计量的完全一致性，并提供了仿真研究以评估理论结果的有限样本性能。