Proves sharp rates E_q(μ_N, ω) ≍ N^{-(1/2)(1 + q/β)} for empirical energy distance approximation under Ahlfors regularity of exponent β.
The equivalence of Fourier-based and Wasserstein metrics on imaging problems.Atti Accademia Nazionale dei Lincei
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Sharp Rates of MMD Empirical Estimation with Power Kernels
Proves sharp rates E_q(μ_N, ω) ≍ N^{-(1/2)(1 + q/β)} for empirical energy distance approximation under Ahlfors regularity of exponent β.