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Keywords:
widely orthant dependent arrays; weighted sums; complete $f$-moment convergence; complete convergence; nonparametric regression models; complete consistency
widely orthant dependent arrays; weighted sums; complete $f$-moment convergence; complete convergence; nonparametric regression models; complete consistency
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.
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