This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent (END, for short) random variables. Some sufficient conditions to prove the strong law of large numbers for weighted sums of END random variables are provided. In particular, the authors obtain the weighted version of Kolmogorov type strong law of large numbers for END random variables as a product. The results that the authors obtained generalize the corresponding ones for independent random variables and some dependent random variables. As an application, the authors investigate the errors-in-variables (EV, for short) regression models and establish the strong consistency for the least square estimators. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for illustration.

本文主要研究扩展负相关变量（简称END）随机变量的加权和的强收敛性。提供了一些充分的条件来证明END随机变量的加权和的强数定律。特别是，作者获得了END随机变量作为产品的Kolmogorov型强数定律的加权形式。作者获得的结果推广了对应于独立随机变量和一些相关随机变量的结果。作为一种应用，作者研究了变量误差（简称EV）回归模型，并为最小二乘估计量建立了强一致性。