Strong Law of Large Numbers for Weighted Sums of Random Variables and Its Applications in EV Regression Models

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.