ON CENTRAL AND NONCENTRAL LIMIT-THEOREMS IN DENSITY-ESTIMATION FOR SEQUENCES OF LONG-RANGE DEPENDENCE

This paper studies the asymptotic properties of the kernel probability density estimate of stationary sequences which are observed through s ome non-linear instantaneous filter applied to long-range dependent Ga ussian sequences. It is shown that the limiting distribution of the ke rnel estimator can be, in quite contrast to the case of short-range de pendence, Gaussian or non-Gaussian depending on the choice of the band width sequences. In particular, if the bandwidth h(N) for sample of si ze N is selected to converge to zero fast enough, the usual root Nh(N) rate asymptotic normality still holds.