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arXiv · 1901.04127

The Bahadur representation for sample quantiles under dependent sequence

Wenzhi Yang·Shuhe Hu·Xuejun Wang
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Abstract

On the one hand, we investigate the Bahadur representation for sample quantiles under $\varphi$-mixing sequence with $\varphi(n)=O(n^{-3})$ and obtain a rate as $O(n^{-\frac{3}{4}}\log n)$, $a.s.$. On the other hand, by relaxing the condition of mixing coefficients to $\sum\nolimits_{n=1}^\infty\varphi^{1/2}(n)<\infty$, a rate $O(n^{-1/2}(\log n)^{1/2})$, $a.s.$, is also obtained.

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Wenzhi Yang, Shuhe Hu, Xuejun Wang. 2019-01-14. The Bahadur representation for sample quantiles under dependent sequence. https://arxiv.org/abs/1901.04127

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