Strong convergence properties for weighted sums of WNOD random variables and its applications in nonparametric regression models

Abstract

In this article, the complete convergence for the maximum of weighted sums of widely negative orthant dependent (WNOD, in short) random variables is investigated under some suitable moment conditions. Some sufficient conditions to prove the complete convergence are provided. The results obtained in the paper generalize some corresponding ones for some dependent random variables. As an application, the complete consistency for the weighted estimator in a nonparametric regression model is established. Finally, we present some simulations to show the consistency for the nearest neighbour weight function estimator in a nonparametric regression model.

Keywords:

• Widely negative orthant dependent random variables
• complete convergence
• nonparametric regression model
• complete consistency

Mathmatics Subject Classifications:

• 60F15
• 62G20

Acknowledgments

The authors are most grateful to the Editor and anonymous referee for carefully reading the manuscript and valuable suggestions which helped in improving an earlier version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Supported by the National Natural Science Foundation of China [11871072, 11701005], the Natural Science Foundation of Anhui Province [1808085QA17] and the Provincial Natural Science Research Project of Anhui Colleges [KJ2019A0003].