A note on weak law of large numbers for weighted sums of negatively associated random variables and an application

This paper establishes novel theoretical results concerning weighted sums of negatively associated random variables, specifically demonstrating both the weak law of large numbers and its corresponding convergence rate. The research findings are subsequently applied to derive complete characterizations (both sufficient and necessary conditions) for the weak consistency property of least squares estimators in simple linear errors-in-variables (EV) regression frameworks. The obtained theorems not only fill certain gaps in existing literature but also provide enhanced versions of some previously known results in this field.