A Class of Rényi Information Estimators for Multidimensional Densities ## AbstractA class of estimators of the R\'enyi and Tsallis entropies of an unknown distribution $f$ in $\mathbb{R}^m$ is presented, based on $k$-th nearest-neighbor distances in a sample of $N$ i.i.d.\ vectors distributed with $f$. We show that entropies of any order $q$ can be estimated consistently with minimal assumptions on $f$. The method can be extended straightforwardly to the estimation of the statistical distance between two distributions using one i.i.d.\ sample from each.
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