Complete moment convergence for m-END random variables with application to non-parametric regression models

Abstract

In this paper, we study the complete moment convergence for arrays of rowwise m-extended negatively dependent (m-END) random variables, which generalizes some corresponding ones for complete convergence. We also give an application to non-parametric regression model based on m-END errors by using the complete convergence that we establish. Finally, the choice of the fixed design points and the weight functions for the nearest neighbor estimator are proposed. We also provide a numerical simulation to verify the validity of our theoretical result.

Keywords:

• m-extended negatively dependent random variables
• complete moment convergence
• complete convergence
• complete consistency
• non-parametric regression models

MATHEMATICAL SUBJECT CLASSIFICATION:

• 60F15
• 62G05
• 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 paper.

Additional information

Funding

This work is 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), the Project on Reserve Candidates for Academic and Technical Leaders of Anhui Province (2017H123) and the Students Innovative Training Project of Anhui University (201810357204).