In this article, we discuss the method of linear kernel quantile estimator proposed by Parzen (1979). We establish a Bahadur representation in sense of almost surely convergence with the rate log-an under the case of S-mixing random variable sequence which was proposed by Berkes (2009). We also obtain the strong consistence of this estimator and its convergence rate.
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Guangxi Normal Univ, Dept Math, Guilin 541004, Peoples R China
Guilin Normal Coll, Dept Math & Comp, Guilin 541001, Peoples R ChinaGuangxi Normal Univ, Dept Math, Guilin 541004, Peoples R China
Wei, Xianglan
Yang, Shanchao
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Guangxi Normal Univ, Dept Math, Guilin 541004, Peoples R China
Guilin Normal Coll, Dept Math & Comp, Guilin 541001, Peoples R ChinaGuangxi Normal Univ, Dept Math, Guilin 541004, Peoples R China
Yang, Shanchao
Yu, Keming
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Brunel Univ, Dept Math Sci, Uxbridge UB8 3PH, Middx, EnglandGuangxi Normal Univ, Dept Math, Guilin 541004, Peoples R China
Yu, Keming
Yang, Xin
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Kings Coll London, Sch Phys Sci & Engn, London, EnglandGuangxi Normal Univ, Dept Math, Guilin 541004, Peoples R China
Yang, Xin
Xing, Guodong
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Hunan Univ Sci & Engn, Dept Math, Yongzhou 425100, Hunan, Peoples R ChinaGuangxi Normal Univ, Dept Math, Guilin 541004, Peoples R China