Reviews: Minimax Estimation of Maximum Mean Discrepancy with Radial Kernels

The paper is very interesting as it provides the first known lower bounds for the minimax rate of estimation of the MMD distance between two distributions based on finite random samples, considering general radial kernels, which match with the known upper bounds up to constants. Theses bounds lead to a classical parametric rate of estimation, not depending on the dimension of the data. The text could however be more fluent, and easier to read for nonspecialists of the minimax estimation theory. For instance, the results are all expressed with respect to the minimax probabilities. Could the link with the more classical minimax risk be clearly written?