Reviews: An adaptive nearest neighbor rule for classification

After reading the author feedback, I am increasing my score as the authors have largely addressed my main concern of comparison/relating to existing locally adaptive NN estimators. The authors address this concern on the theory side. I still think additional numerical experiments to compare the proposed method with other adaptive NN approaches would strengthen the paper and be beneficial to practitioners (and could possibly lead to interesting theoretical questions if, for instance, there are some surprising performance gaps). The analysis is quite clean and elegant due to the newly introduced local notion of "advantage" as an alternative to the usual local Lipschitz conditions. The paper, however, does not discuss enough related work, especially adaptive nearest neighbor and kernel methods based on Lepski's method (for example, the adaptive k-NN method by Kpotufe (2011)).