Bahadur Representation of Linear Kernel Quantile Estimator for Stationary Processes

In this article, we discuss the method of linear kernel quantile estimator proposed by Parzen (1979 Parzen, E. (1979). Nonparametric statistical data modeling. J. Amer. Statist. Assoc. 74:105121.Taylor &; Francis Online], Web of Science ®] , Google Scholar]). We establish a Bahadur representation in sense of almost surely convergence with the rate log^{? α}n under the case of S-mixing random variable sequence which was proposed by Berkes (2009 Berkes, I., Hörmann, S., (2009). Asymptotic results for the itpirical process of stationary sequences. Stoch. Process. Their Applic. 119:12981324.Crossref], Web of Science ®] , Google Scholar]). We also obtain the strong consistence of this estimator and its convergence rate.