Reviewer 1: There are (at least) two reasons to justify the averaging over a ball of radius γ > 0 around x

We would like to thank all referees for their appreciation of our results and the useful feedback. Example 3.2 indicates that when γ = 0, the estimator may be inconsistent. Second, Example 3.3 shows that we can recover the k-nearest neighbors by choosing γ To improve the transparency of our estimator, we will provide in the revision a description of the worst-case distribution. We agree that this information should be made more explicit to the readers. Thank you for pointing out the relevant literature.