  The R\'enyi entropy is a generalization of the Shannon entropy and is widely
used in mathematical statistics and applied sciences for quantifying the
uncertainty in a probability distribution. We consider estimation of the
quadratic R\'enyi entropy and related functionals for the marginal distribution
of a stationary m-dependent sequence. The U-statistic estimators under study
are based on the number of epsilon-close vector observations in the
corresponding sample. A variety of asymptotic properties for these estimators
are obtained (e.g., consistency, asymptotic normality, Poisson convergence).
The results can be used in diverse statistical and computer science problems
whenever the conventional independence assumption is too strong (e.g.,
epsilon-keys in time series databases, distribution identification problems for
dependent samples).
