Berry–Esseen bounds for kernel estimates of stationaryprocesses

In this paper we obtain nonuniform Berry–Esseen bounds of the kernel estimate of stationary process {Xi} by the method of martingale approximation. In particular, by choice of bandwidth bn, the Berry–Esseen bounds can be n − 2 / 15 . The dependence condition of {Xi} is expressed in terms of physical dependence measures introduced by Wu (2005).