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

Estimation of quadratic density functionals under m-dependence