摘要
On the one hand,we investigate the Bahadur representation for sample quantiles underφ-mixing sequence withφ(n)=O(n^-3)and obtain a rate as O(n-3/4 log n),a.s.On the other hand,by relaxing the condition of mixing coefficients to∑∞n=1φ^1/2(n)<∞,a rate O(n^-1/2(log n)^1/2),a.s.,is also obtained.
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 log n), a.s. On the other hand, by relaxing the condition of mixing coefficients to■, a rate O(n-1/2（log n）1/2), a.s., is also obtained.
基金
Supported by NNSF of China(11501005,11671012,11701004,11701005)
NSF of Anhui Province(1808085QA03,1808085QA17,1808085QF212)
Provincial Natural Science Research Project of Anhui Colleges(KJ2017A027,KJ2018A0030)
