Berry–Esseen bounds for kernel estimates of stationaryprocesses

Abstract

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