  In this paper, we study estimation of certain integral functionals of one or
two densities with samples from stationary m-dependent sequences. We consider
two types of U-statistic estimators for these functionals that are functions of
the number of epsilon-close vector observations in the samples. We show that
the estimators are consistent and obtain their rates of convergence under weak
distributional assumptions. In particular, we propose estimators based on
incomplete U-statistics which have favorable consistency properties even when
m-dependence is the only dependence condition that can be imposed on the
stationary sequences. The results can be used for divergence and entropy
estimation, and thus find many applications in statistics and applied sciences.
