Asymptotic weak convergence holds for functionals of the empirical entropic optimal transport plan, supporting uniform confidence bands for colocalization curves via Hadamard differentiability and the delta method.
Denote, with abuse of notation, byξthe operator onC b(X)× C b(X)defined byξ(f, g)(x, y), where x, y∈ X
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Distributional Convergence of Empirical Entropic Optimal Transport and Statistical Applications
Asymptotic weak convergence holds for functionals of the empirical entropic optimal transport plan, supporting uniform confidence bands for colocalization curves via Hadamard differentiability and the delta method.