A class of estimators of the Rényi and Tsallis entropies of an unknown distribution f in R m is presented. These estimators are based on the kth nearest-neighbor distances computed from a sample of N i.i.d. vectors with distribution f . We show that entropies of any order q, including Shannon's entropy, can be estimated consistently with minimal assumptions on f . Moreover, we show that it is straightforward to extend the nearest-neighbor method to estimate the statistical distance between two distributions using one i.i.d. sample from each.
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