Complete moment convergence for weighted sums of widely orthant-dependent random variables and its application in nonparametric regression models

Abstract

We establish some results on the complete moment convergence for weighted sums of widely orthant-dependent (WOD) random variables, which improve and extend the corresponding results of Y. F. Wu, M. G. Zhai, and J. Y. Peng [J. Math. Inequal., 2019, 13(1): 251–260]. As an application of the main results, we investigate the complete consistency for the estimator in a nonparametric regression model based on WOD errors and provide some simulations to verify our theoretical results.

Key words： Widely orthant-dependent random variables; complete moment convergence; nonparametric regression model

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