Bandwidth selection in nonparametric regression with general errors

Abstract

For the equally spaced fixed design nonparametric regression, we use the idea in Haerdle et al. ( J. Amer. Assoc. (1992), 87, 227–233) to construct a bandwidth selector. This bandwidth selector can be applied directly to both the case of independent observations and the case of dependent observations. In applications of this bandwidth selector, there is no need to identify the independence of observations or to estimate the dependence structure of observations. The strong consistency and the limiting distribution of the bandwidth produced by this bandwidth selector are given. For independent observations, this limiting distribution is the same as that of the cross-validated bandwidth given in Haerdle et al. ( J. Amer. Assoc. (1988) 83, 86–101). On the other hand, for dependent observations, this limiting distribution is the same as those of the bandwidths produced by modified Mallows' criterion given in Chiu ( Statist. Probab. Lett. (1989) 8, 347–354) and Hart ( J. Roy. Statist. Soc. (1991) 53, 173–187).