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We provide finite-sample analysis of a general framework for using k-nearestneighbor statistics to estimate functionals of a nonparametric continuousprobability density, including entropies and divergences. Rather than plugginga consistent density estimate (which requires $k \to \infty$ as the sample size$n \to \infty$) into the functional of interest, the estimators we consider fixk and perform a bias correction. This is more efficient computationally, and,as we show in certain cases, statistically, leading to faster convergencerates. Our framework unifies several previous estimators, for most of whichours are the first finite sample guarantees.

Finite-Sample Analysis of Fixed-k Nearest Neighbor Density Functional Estimators