Weak convergence of empirical Wasserstein type distances

Philippe Berthet, Jean-Claude Fort

We estimate contrasts ${\int }_0^1\rho (F^{-1}(u)-G^{-1}(u))du$ between two continuous distributions $F$ and $G$ on $\mathbb{R}$ such that the set $\{F=G\}$ is a finite union of interval…