Convergence rate for weighted sums of ψ-mixing random variables and applications

Abstract

The complete convergence result is obtained for weighted sums of ψ -mixing random variables without any conditions on mixing rate. As a special case, we can obtain the law of large numbers of Liu and Jin (J. Math. Ineq., 12, 2018). As applications, necessary and sufficient conditions are provided for the complete consistency of LS estimators in the errors-in-variables regression model with ψ -mixing errors.