Weak convergence for weighted sums of negatively associated random variables and its application in nonparametric regression models

Abstract

In this paper, we mainly study the weak convergence and convergence rates in the weak law of large numbers for weighted sums of negatively associated random variables. The necessary and sufficient conditions for the convergence rates in the weak law of large numbers are provided. As an application, the weak consistency for the weighted linear estimator of nonparametric regression models is established. Some numerical simulations are also provided to verify the validity of the theoretical result.

KEYWORDS:

• Convergence rate
• Negatively associated random variables
• Nonparametric regression models
• Weak consistency
• Weak law of large numbers

MATHEMATICAL SUBJECT CLASSIFICATION:

• 60F05
• 62G20

Acknowledgements

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 article.

Additional information

Funding

Supported by the National Natural Science Foundation of China (11671012, 11871072, 11701004, 11701005), the Natural Science Foundation of Anhui Province (1808085QA03, 1908085QA01, 1908085QA07), the Provincial Natural Science Research Project of Anhui Colleges (KJ2019A0003) and the Project on Reserve Candidates for Academic and Technical Leaders of Anhui Province (2017H123).