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Eberly College of Arts and Sciences




A consistent entropy estimator for hyperspherical data is proposed based on the k-nearest neighbor (knn) approach. The asymptotic unbiasedness and consistency of the estimator are proved. Moreover, cross entropy and Kullback-Leibler (KL) divergence estimators are also discussed. Simulation studies are conducted to assess the performance of the estimators for models including uniform and von Mises-Fisher distributions. The proposed knn entropy estimator is compared with the moment based counterpart via simulations. The results show that these two methods are comparable.

Source Citation

Li, S., Mnatsakanov, R. M., & Andrew, M. E. (2011). k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions. Entropy, 13(3), 650–667.


2011 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (


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