Strong laws for weighted sums of $$\psi $$ ψ -mixing random variables and applications in errors-in-variables regression models

Abstract

In this paper, we establish strong laws for weighted sums of identically distributed $$\psi $$ -mixing random variables without any conditions on mixing rate. The classical Kolmogorov strong law of large numbers is extended to weighted sums of $$\psi $$ -mixing random variables. Two types of weights are considered for the weighted sums. These results are applied to the least-squares estimators in the simple linear errors-in-variables regression model when the errors are $$\psi $$ -mixing random vectors.