A class of estimators of the Rényi and Tsallis entropies of an unknown distribution f in ℝm 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.

This paper proposes a new class of estimators of an unknown entropy of random vector. Its asymptotic unbiasedness and consistency are proved. Further, this class of estimators is used to build both goodness-of-fit and independence tests based on sample entropy. A simulation study indicates that the test involving the proposed entropy estimate has higher power than other well-known competitors under heavy tailed alternatives which are frequently used in many financial applications.