Central Limit Theorem and bootstrap procedure for Wasserstein's variations with application to structural relationships between distributions

Finally, the semidiscrete framework provides a control on the second derivative of the dual formulation, which yields the first central limit theorem for the optimal

However, our ap- proach to prove uniquess and stability of optimal transportation potentials relies on tools from the theory of graphical convergence of multivalued maps (a

The proof is based on a new central limit theorem for dependent sequences with values in smooth Banach spaces, which is given in Section 3.1.1.. In Section 2.2, we state the

We give two main results, which are necessary tools for the study of stability in section 3: we prove uniqueness, up to an additive constant, of the optimal transport

As a matter of fact, the statistical analysis of the estimates and their asymptotic behaviour in distribution require a particular study of the asymptotic expan- sion of M n that

Central Limit Theorems- Generelized Wasserstein distances- Empirical processes- Strong approximation- Dependent samples..

Central limit theorems for the Wasserstein distance between the empirical and the true distributions. Correction: “Central limit the- orems for the Wasserstein distance between

It is known that Efron’s resampling bootstrap of the mean of random variables with common distribution in the domain of attraction of the stable laws with infinite vari- ance is