In this paper, we establish strong laws for weighted sums of identically
distributed ψ-mixing random variables without any conditions on mixing rate. The
classical Kolmogorov strong law of large numbers is extended to weighted sums of
ψ-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 ψ-mixing random vectors.

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