Maximal moment inequalities for partial sums of ρ-mixing random variables with application to conditional value-at-risk estimator

Abstract

Maximal moment inequalities for partial sums of ρ-mixing random variables are established, which use some moment summations as upper bound. As application, we investigate strong consistency of conditional value-at-risk estimator for ρ-mixing samples and give the corresponding convergence rate.

Keywords:

• Maximal moment inequalities
• ρ-mixing
• conditional value-at-risk
• strong consistency
• convergence rate

Mathematics Subject Classification (2000):

• 60G05
• 62G20

Acknowledgments

The authors are greatly grateful to the anonymous referee for providing valuable suggestions which improved the first manuscript.

Additional information

Funding

This research was supported by the Important Natural Science Foundation of Colleges and Universities of Anhui Province (No. KJ2020A0122), the Achievements on the special project of provincial scientific research platform of Hefei Normal University (No. 2020PT25), the Natural Science Foundation of China (No. 12001105) and the Postdoctoral Science Foundation of China (2019M660156).