In this paper, the complete moment convergence for weighted sums of (α,β )-mixingrandom variables is investigated. The result improves and extends the corresponding one of Wuet al. (2017). As a corollary, the complete convergence for weighted sums of (α,β )-mixingrandom variables is obtained, which is applied to establish the complete consistency for the P-Cestimator in a nonparametric regression model.
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