Complete f-moment convergence for sums of asymptotically almost negatively associated random variables with statistical applications

Abstract

In this paper, we mainly study the complete f-moment convergence for sums of asymptotically almost negatively associated (AANA, for short) random variables and provide an application. A general result on complete f-moment convergence for arrays of rowwise AANA random variables is obtained. We also give an application to nonparametric regression models based on AANA errors by using the result on complete f-moment convergence that we have established. A sufficient and necessary moment condition for the complete consistency is presented. Finally, a numerical simulation is provided to verify the validity of the theoretical result.

Keywords:

• Asymptotically almost negatively associated random variables
• complete f-moment convergence
• complete convergence
• nonparametric regression model
• complete consistency

Mathematical subject classifications:

• 60F15
• 62G05

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 author(s).

Additional information

Funding

Supported by the National Social Science Foundation of China (22BTJ059).