In this paper, the Marcinkiewicz-Zygmund type strong law is established for weighted sums of \( \psi \) -mixing random variables without any conditions on mixing rate. Furthermore, necessary condition for the established strong law is also derived. As corollaries of the main result, some corresponding results of classical summability methods are obtained. To prove the main result, the Hoffmann-Jørgensen inequality is extended for \( \psi \) -mixing sequences, which is of great importance. The result obtained generalizes the well-known results from independent random variables to \(\psi \) -mixing case. As its applications, strong consistency is obtained for the least squares estimators in the simple linear errors-in-variables model and the weighted estimator in the nonparametric regression model, and some numerical simulations are provided to verify the validity of theoretical results.
