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.
Equivalence of distance-based and RKHS-based statistics in hypothesis testing.The Annals of Statistics, 41(5):2263–2291, October 2013
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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.