Reviews: The Nearest Neighbor Information Estimator is Adaptively Near Minimax Rate-Optimal

Paper 1614 This paper studies the Kozachenko-Leonenko estimator for the differential entropy of a multivariate smooth density that satisfy a periodic boundary condition; an equivalent way to state the condition is to let the density be defined on the [0,1] d-torus. The authors show that the K-L estimator achieves a rate of convergence that is optimal up to poly-log factors. The result is interesting and the paper is well-written. I could not check the entirety of the proof but the parts I checked are correct. I recommend that the paper be accepted.