Complete convergence for weighted sums of WNOD random variables and its applications

ABSTRACT

In this paper, we mainly studied the complete convergence for weighted sums of widely negative orthant dependent (WNOD, in short) random variables. Some sufficient conditions to prove the complete convergence are provided. As an application, the complete consistency for the weighted estimator of nonparametric regression model is established, and the simulation study is provided to evaluate the finite sample performance of the consistency for the nearest neighbour weight function estimator.

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, 11501004) and the Natural Science Foundation of Anhui Province (1508085J06, 1608085QA02).