Reviews: Finite-Sample Analysis of Fixed-k Nearest Neighbor Density Functional Estimators

There are some issues with the conditions imposed on distributions in this paper. In particular, regarding the local bound hypothesis: in the proof of Lemma 2 epsilon may depend on x, so p * will be smaller than stated. As an example, if p(x) goes to 0 as x a when x goes to 0, then p *(x) goes to 0 as x (a 1). AFTER REBUTTAL: 1) The rebuttal here is helpful, but there seem to still be some issues with the local lower bounds hypothesis. They claim that it is very mild in light of Lemma 2, but Lemma 2 doesn't apply very well to the situation of p x a. I think that they should at least include what they've written in the rebuttal.