Abstract

By using the Marcinkiewicz-Zygmund type inequality and Rosenthal type inequality, we study the L_r convergence, weak law of large numbers and the complete convergence for usual normed sums and weighted sums of arrays of rowwise widely orthant dependent (WOD, for short) random variables. In addition, some applications of the L_r convergence and the complete convergence to nonparametric regression models based on WOD errors are provided. At last, we provide a numerical simulation to verify the validity of our theoretical result.

中文翻译：

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WOD随机变量的大数定律和完全收敛性及其应用

摘要

通过使用Marcinkiewicz-Zygmund型不等式和Rosenthal型不等式，我们研究了L _r 收敛，大数弱定律以及行范数正态相关（随机称为WOD）的常规范数总和和加权和的完全收敛变量。此外，还提供了L _r 收敛和完全收敛在基于WOD误差的非参数回归模型中的一些应用。最后，我们提供了一个数值模拟来验证我们理论结果的有效性。