\(K\)-nearest neighbor based consistent entropy estimation for hyperspherical distributions (Q657553)

Summary: 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.