A Note on the Berry-Esséen Bound of Sample Quantiles for ϕ-mixing Sequence

Abstract

By using martingale method and properties of ϕ-mixing random variables, we go on studying the Berry-Esséen bound of sample quantiles for ϕ-mixing sequence and improve the rate O(n^{− 1/9}) to O(n^{− 1/6} · log n · log log n), where the mixing coefficients relax to . It improves the corresponding result.

Keywords:

• Berry-Esséen bound
• Sample quantile
• ϕ-mixing random variable

Mathematics Subject Classification:

• 62F12
• 62E20
• 60F05

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (11171001, 11201001), Natural Science Foundation of Anhui Province (1208085QA03, 1408085QA02), Higher Education Talent Revitalization Project of Anhui Province (2013SQRL005ZD), Academic and Technology Leaders to Introduction Projects of Anhui University and Applied Teaching Model Curriculum of Anhui University (XJYYKC1401).