In this paper, a general result on complete moment convergence for arrays of rowwise negatively orthant dependent random variables is obtained. In addition, we present some sufficient conditions to prove the complete moment and complete convergences for the variables. As applications, the complete consistency for the estimators of nonparametric and semiparametric regression models based on negatively orthant dependent errors is established by using the complete convergence that we established. A simulation to study the numerical performance of the consistency for the nearest neighbor weight function estimator in semiparametric regression model is given. Our results generalize and improve some corresponding ones for independent random variables and negatively associated random variables.

中文翻译：

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负正交相关随机​​变量的完全矩收敛及其在统计模型中的应用

在本文中，获得了行向负正交相关随机​​变量数组的完全矩收敛的一般结果。此外，我们提出了一些充分条件来证明变量的完全矩和完全收敛。作为应用，利用我们建立的完全收敛性，建立了基于负正交相关误差的非参数和半参数回归模型估计量的完全一致性。仿真研究了半参数回归模型中最近邻权函数估计器的一致性的数值性能。我们的结果对独立随机变量和负相关随机变量的一些相应结果进行了概括和改进。