Complete \(f\)-moment convergence for weighted sums of WOD arrays with statistical applications. (English) Zbl 07675640

Summary: Complete \(f\)-moment convergence is much more general than complete convergence and complete moment convergence. In this work, we mainly investigate the complete \(f\)-moment convergence for weighted sums of widely orthant dependent (WOD, for short) arrays. A general result on Complete \(f\)-moment convergence is obtained under some suitable conditions, which generalizes the corresponding one in the literature. As an application, we establish the complete consistency for the weighted linear estimator in nonparametric regression models. Finally, some simulations are provided to show the numerical performance of theoretical results based on finite samples.


60F15 Strong limit theorems
62G20 Asymptotic properties of nonparametric inference
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