Complete moment convergence for randomly weighted sums of END sequences and its applications

Abstract

In this article, some results on the complete moment convergence for maximal randomly weighted sums of extended negatively dependent (END) random variables are established. In some senses, the results obtained in this article extend the corresponding ones of in reference. As an application of the main results, we consider a result on complete consistency for the weighted estimator in a non parametric regression model based on END errors. We also give a simulation to verify the validity of the theoretical result.

Keywords:

• Extended negatively dependent
• complete moment convergence
• complete convergence
• Non parametric regression model

MATHEMATICS SUBJECT CLASSIFICATION:

• 60F15
• 62G05

Acknowledgments

The authors are most grateful to the editor and anonymous referees for their careful reading of the manuscript and many valuable suggestions which helped to improve an earlier version of this article.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (No. 11701403, 71803140).