The Bahadur representation for sample quantiles under dependent sequence

01/14/2019

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by   Wenzhi Yang, et al.

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On the one hand, we investigate the Bahadur representation for sample quantiles under φ-mixing sequence with φ(n)=O(n^-3) and obtain a rate as O(n^-3/4 n), a.s.. On the other hand, by relaxing the condition of mixing coefficients to ∑_n=1^∞φ^1/2(n)<∞, a rate O(n^-1/2( n)^1/2), a.s., is also obtained.