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Abstract
Under some weak conditions, we use the moment inequality for -mixing sequence to investigate the Bahadur representation of sample quantiles based on this stochastic sequence. For all
, we obtain a rate of Bahadur representation in the form of
, which is close to the rate
.
AMS SUBJECT CLASSIFICATION:
Acknowledgements
The authors are deeply grateful to Editor, Associate Editor and third anonymous referees for their careful reading and insightful comments, which helped in improving an earlier version of this paper.
Notes
No potential conflict of interest was reported by the authors.
Additional information
Funding
This work is supported by the National Natural Science Foundation of China [grant number 11171001], [grant number 11426032], [grant number 11501005]; Natural Science Foundation of Anhui Province [grant number 1408085QA02], [grant number 1508085J06]; Provincial Natural Science Research Project of Anhui Colleges [grant number KJ2014A020]; Higher Education Talent Revitalization Project of Anhui Province [grant number 2013SQRL005ZD]; Academic and Technology Leaders to Introduction Projects of Anhui University.