On the Bahadur representation of sample quantiles for ψ-mixing sequences and its application

ABSTRACT

In this paper, the Bahadur representation of sample quantiles for ψ-mixing sequences is obtained under the given conditions. As its application, the uniformly asymptotic normality is derived.

Keywords:

• ψ −mixing sequence
• Bahadur representation
• Sample quantile
• Uniformly asymptotic normality

Acknowledgments

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

Additional information

Funding

This research is supported by the Key Disciplines for Operational Research and Cybernetics of the Education Department of Guangxi Province, the National Science Foundation of China(11461009) and the Natural Science Foundation of Guangxi (2011GXNSFA018133).