Nonparametric estimation of a regression function with dependent observations

This paper investigates performance of nonparametric kernel regression and its associated bandwidth selection for dependent observations. For short range dependent observations, it is shown that the convergence rate of asymptotic normality and the strong uniform convergence rate (SUCR) of the kernel estimator are of the same orders as those given for the case of independent observations. Also, Mallows' criterion is adjusted to correct for the effect of dependence on bandwidth selection. The bandwidth produced by modified Mallows' criterion is analyzed by a central limit theorem. The convergence rate of the bandwidth is of the same order as that given for the case of independent observations. On the other hand, for long range dependent observations, the SUCR of the kernel estimator could be slower or faster than that given for the case of independent observations, depending on the dependence structure.