A claimed proof that a relative-entropy threshold test is asymptotically optimal for two-sample testing is invalid due to a sign error and an incorrect Rényi-divergence identity; the one-sample re-derivation is sound.
Asymptotically optimal one-and two-sample testing with kernels
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Asymptotically Optimal Tests for One- and Two-Sample Problems
A claimed proof that a relative-entropy threshold test is asymptotically optimal for two-sample testing is invalid due to a sign error and an incorrect Rényi-divergence identity; the one-sample re-derivation is sound.