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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper presents the first finite sample analysis of k-NN density estimation and mode estimation. The paper is well-written and the results are novel and appear to be correct. I think the results are quite impressive and, because mode estimation plays an important role in density-based clustering, the results are important. My only negative comment is that there are no numerical experiments.